Morrison was born in Hammond, the principal city of Tangipahoa Parish, one the "Florida Parishes" east of the capital city of Baton Rouge, to banker-merchant Benjamin M. Morrison and the former Florence Hobson (1878–1972) of Greensboro in Hale County in the western Black Belt of Alabama. A maternal uncle, Richmond Pearson Hobson was a naval hero of the Spanish–American War and later served five terms in the U. S. House from Alabama.
Morrison attended public schools and obtained the Juris Doctor degree from Tulane University Law School in New Orleans in 1934. He practiced law in Hammond with Joseph A. Sims, later an aide to Governor Earl Kemp Long.
In 1940, Morrison married the former Marjorie Abbey (November 1916 – January 25, 2016) of Webb in Tallahatchie County in northwestern Mississippi. A graduate of Mary Baldwin College in Staunton, Virginia, and an advocate of the arts who did post-graduate studies at the New York School of Interior Design, Mrs. Morrison was the daughter of Thomas Benton and Julia Cochran Abbey. The couple had two sons, James Hobson Morrison, Jr. (born November 1942), and wife, Lisa, of Hammond, and Benjamin Abbey Morrison (born July 1944) of New Orleans.
In 1936, Morrison ran for the Louisiana State Senate, losing by a narrow margin. He alleged vote fraud, and although he did not take office, from then until he was elected to Congress commonly billed himself as "Senator Jim Morrison". In 1937, Morrison wrote the charter of the newly formed Louisiana Farmers Protective Union and launched a public relations campaign on behalf of union members in the strawberry belt centered about Tangipahoa Parish.
In his first election to Congress in 1942, Morrison defeated the conservative incumbent, Jared Y. Sanders, Jr., in the Democratic primary. He was unopposed in the general election of 1942 as well as the elections of 1944 and 1946. He secured a total of twelve terms before Rarick, then a state district court judge defeated him in the 1966 primary, 51.2 to 48.8 percent.
After the end of World War II, Morrison introduced a bill to grant U.S. citizenship to New Orleans Mafia boss "Silver Dollar Sam" Carolla in order to prevent Carolla's deportation. Though he signed the Southern Manifesto and later joined all Louisiana congressional delegation members in voting against the Civil Rights Act of 1964, Morrison was considered politically liberal during the 1960s because of his support for many federal social programs.
Earlier in his career, Morrison was the only member of the Louisiana congressional delegation to oppose the 1947 Taft-Hartley Act, which outlawed forced labor union membership.
On November 8, 1960, Republicans offered the native Pennsylvanian, Charles H. Dillemuth (February 18, 1912 – August 29, 1989) as their nominee against Morrison. A Baton Rouge businessman with an impressive war record for whom a local humanitarian award is named, Dillemuth polled only 14.4 percent of the vote.
In 1964, the Republican businessman Floyd O. Crawford (October 28, 1907 – January 4, 1995) of Baton Rouge, formerly from Illinois, ran a stronger race than had Dillemuth. However, Crawford too was defeated, 48,715 (37.1 percent) to Morrison's 82,686 (62.9 percent). Crawford was aided by the presence of Barry M. Goldwater at the top of the GOP ticket, and he won majorities in three parishes near Baton Rouge, East Feliciana, West Feliciana, and St. Helena — all obtained in the year prior to adoption of the pivotal Voting Rights Act of 1965, which would thereafter turn all three of those predominantly African American parishes into Democratic strongholds.
Crawford's modest but burgeoning support may have encouraged stronger opposition to Morrison to emerge in 1966. Another factor was Morrison's support of the aforementioned Voting Rights Act of 1965, followed by a so-called "backlash" of new white registrants who in some cases neutralized the effect of increased voting registration by blacks.
On three occasions, Morrison ran unsuccessfully for governor — 1940 (polling 48,243 votes or 8.7 percent and losing to the eventual winner, Sam Houston Jones), 1944 (with 76,081 votes or 15.9 percent and failing to enter the runoff with Jimmie Davis), and 1948 (101,754 votes or 15.8 percent and failing to enter the runoff with the resurgent Earl Long). In 1944, his other opponents were Lewis L. Morgan of Covington, the ticket mate of Earl Long, who unsuccessfully sought the lieutenant governorship that year; Sam Caldwell, the mayor of Shreveport; and colorful State Senator Dudley J. LeBlanc of Abbeville in Vermillion Parish. In 1948, Morrison campaigned for governor with the promise of a soldiers' "bonus". His ticket mates included Lucille May Grace for register of state lands and J.Y. Fontenot for lieutenant governor, but victory that year went to the slate supporting the return to office of former Governor Earl Long. In the gubernatorial races, Morrison could run for governor without sacrificing his U.S. House seat because Louisiana holds gubernatorial elections a year between congressional races.
Morrison was a delegate to the Democratic National Conventions of 1956 and 1960 and supported the Adlai Stevenson and John F. Kennedy tickets, respectively. Morrison was not related to Mayor deLesseps Story Morrison Sr. of New Orleans though the two often agreed politically and both ran unsuccessfully for governor on three occasions. After his defeat for Congress, Morrison resumed his law practice in Hammond. Rarick served in the House seat from 1967 to 1975, a third of the tenure that Morrison accumulated.
Morrison died of a heart attack after a series of strokes. His last residence was in Loranger in central Tangipahoa Parish. He is interred at the Episcopal Church Cemetery in Hammond. U.S. 51, a main north-south thoroughfare through Hammond, was renamed Morrison Boulevard in honor of the congressman.
Morrison donated his congressional papers to the Archives and Special Collections Department of Southeastern Louisiana University in Hammond. His photographic collection of national leaders, family, and campaign events are displayed in the Linus A. Sims Memorial Library in what is called the "Morrison Room". Linus A. Sims, the founder of Southeastern University, was the father of Morrison's former law partner, Joseph Sims. After the donation of his papers to SLU, Morrison valued this donation at $1.6 million and attempted to take an income tax reduction of over $61,100 over a five-year period. The United States Tax Court held that Morrison failed to establish the claimed deduction. On appeal, the Fifth Circuit Court of Appeals affirmed the decision of the Tax Court.
Morrison patronized the Center for Southeast Louisiana Studies at Southeastern University. In 1995, Dr. John Miller, dean of the College of Arts and Sciences, inaugurated the annual James H. Morrison Lecture on Politics and Government at Southeastern. Political figures from both parties have delivered Morrison lectures, including former Democratic U.S. Senator John B. Breaux and Jack A. "Jay" Blossman, Jr., the Republican former chairman of the Louisiana Public Service Commission.