After graduating from the local school in 1960 Oleksandr Moroz graduated from the Agricultural Academy of the Ukrainian SSR becoming a mechanical engineer. Then he worked in many careers, including as a teacher and engineer for twelve years, and joined the Communist Party of the Soviet Union, moving from the First Secretary of local Regional Committee of the CPSU to the position of the Head of the Kiev Oblast Committee and the Oblast Trade Union Committee. He was a recipient of the Medal "For Labour Valour". He was a member of the Communist Party of the Soviet Union from 1972 to 1991. He became a deputy of Verkhovna Rada (Ukraine's parliament) in 1990. During the August 1991 Declaration of Independence of Ukraine Moroz was Communist majority leader in the Verkhovna Rada.
On 26 October 1991, he arranged the congress that formed the Socialist Party of Ukraine (SPU) as a successor of the Communist Party (Bolsheviks) of Ukraine.
Moroz ran as a presidential candidate as a nominee of the Socialist Party of Ukraine in the 1994 and 1999 elections, he came third both times, with 13.04% of the vote in 1994 and 11.29% in 1999. In 1999, many experts predicted that Moroz had a chance to defeat incumbent Leonid Kuchma in the election run-off and according to many observers the government rigged the election results in favor of Petro Symonenko (of the Communist Party of Ukraine) in order to make sure that unpopular Symonenko, rather than Moroz, would compete against Kuchma in the run-off vote.
In 1996, Moroz together with several other parties prevented President Leonid Kuchma's attempt to concentrate most of the powers in the president's hands and led the parliament to adopt on 28 June the new Constitution that includes many positions close to the demands of left parties. In 1999 after signing the treaty of "Kanev Four" he became an acknowledged leader of the non-Communist opposition to Kuchma.
In 2001 Moroz at a sitting of the Verkhovna Rada made public "Mykola Melnychenko’s tapes" that alleged the involvement of the top leaders of the state (including president Kuchma) in the murder of famous independent journalist Georgiy Gongadze that provoked the political crisis in Ukraine known as the Cassette Scandal. Moroz was a member of a special board "Forum of national salvation", a representative of a Public Committee of Protection of the Constitution "Ukraine Without Kuchma" (and later "Rise, Ukraine!") in charge of negotiations with representatives of the regime.
In 2002 the Socialist Party of Ukraine (which included Yuriy Lutsenko, Josef Vinski, Mykola Rudkovski, Valentyna Semenyuk) got the fourth place in the Ukrainian parliamentary election, 2002. The socialists joined the “oppositional four” a group of parties that also included Our Ukraine, Yulia Tymoshenko Electoral Bloc and Communist Party of Ukraine.
In the 2004 Ukrainian presidential election, Moroz was nominated by the Socialist Party of Ukraine, which he has chaired since 1991. He won third place with 5.81% of the vote. As a longtime leader of anti-Kuchma forces, Moroz quickly announced his support for Viktor Yushchenko's presidential bid against Kuchma's prime minister, Viktor Yanukovich, thus making Yushchenko the favourite to win in round two. That Yushchenko did not win despite this endorsement was used to argue that there was election fraud in the run-off. Moroz supported the subsequent Orange Revolution, the mass protests that eventually led to the annulment of the vote results and to a revote won by Yushchenko. The support of the Ukrainian socialists he brought to Yushchenko's campaign was important to widen Yushchenko's appeal to voters. Similarly, the votes of Moroz's Socialist party faction in Verkhovna Rada (parliament) were crucial for passing several important resolutions during the Orange Revolution, particularly the non-confidence vote in the Kuchma-Yanukovych government involved in election fraud scandal.
After the Ukrainian parliamentary election, 2006 Moroz was elected the Chairman of the Verkhovna Rada of Ukraine on 6 July 2006 (238 ayes, 226 needed for election) with support of the Party of Regions, SPU, and communist factions.
The Socialist Party of Ukraine received 2.86% of the national vote in the Ukrainian parliamentary election, 2007 falling 0.14% below the election threshold denying them the right of representation and removing Moroz as a member of Ukraine's Parliament.
The Socialist Party of Ukraine chose the party leader, Oleksandr Moroz, as their presidential candidate for the 2010 Presidential election, first-round ballot scheduled to be held on January 17, 2010. 268 out of 422 party congress delegates registered supported the Moroz's nomination. During the election Moroz received 0,38% of the votes. Public Opinion Polls did not rated the Socialist Party of Ukraine or its leader Olexandr Moroz as it they were undecided as to their participation in the Ukrainian Presidential election In 2005 Moroz received 5.8% of the national vote. An Opinion polls conducted by FOM-Ukraine in April 2009 showed Moroz with less than 1% support with most analysts not considering Moroz as a serious contender as he would not win sufficient number of votes in the first-round presidential ballot, scheduled for January 17, 2010.
After leading his party for 20 years, in July 2010 he was succeeded as party leader by Vasyl Tsushko. However, Moroz was again elected as party leader in August 2011. In April 2012 Petro Ustenko was elected as Moroz's successor as party leader.
Moroz tried to return to parliament in the 2012 Ukrainian parliamentary election, running as an independent candidate, single-member districts number 93 (first-past-the-post wins a parliament seat) located in Kiev Oblast; but he finished third in this district with 11.94% of the votes.
Since Oleksandr Moroz organized the left-centrist Socialist Party of Ukraine his party ideology largely evolved from orthodox Communism to Social democracy. He himself is a left-wing social democrat of the European type who uses both Marxist and Social democratic ideas. For this reason he met strong opposition from a more rigid wing of his party represented by the supporters of Nataliya Vitrenko. Finally, Vitrenko left the Socialist party, proclaimed the Progressive Socialist Party of Ukraine and bannered Moroz as "Opportunist" and "traitor", much helping Kuchma to fight the opposition of Ukraine of which Moroz' Socialist Party was part. After the last radicals headed by Ivan Chyzh left the party and formed an organization called "Spravedlyvist" ("Justness"), Moroz was able to transform his party closer to the European Social Democratic model.
Moroz and his party supported the political reform and Ukraine's transition towards a more European Parliamentary democracy, which shifted the power balance in Ukraine stripping the President of some of his powers in favor of the parliament. During the Orange Revolution his party voted for the changes to the Ukrainian constitution, changes that made Ukraine a parliamentary and not a presidential republic. This constitution, pushed by Moroz and Petro Simonenko, went into effect in January 2006, despite Yushchenko's furious opposition. Moroz also speaks in support of the preservation of land for Ukrainian farmers and has made many promises about resolving social problems, using socialist rhetoric. The program of his party begins with a statement that demands real democracy for working people.