Dunbar grew up on Brafferton Arbor on the Buttershaw council estate in Bradford with seven brothers and sisters. Both her parents had worked in the textile industry. Dunbar attended Buttershaw Comprehensive School.
Dunbar began her first play The Arbor in 1977 at the age of 15, writing it as a classroom assignment for CSE English. Encouraged by her teacher, she was helped to develop the play to performance standard. It was premiered in 1980 at London's Royal Court Theatre, directed by Max Stafford-Clark. Alongside an entry by Lucy Anderson Jones, It jointly won the Young Writers' Festival, and was later extended and performed in New York. The play described the experiences of a pregnant teenager with an abusive drunken father. On 26 March 1980, she was featured in the BBC's Arena arts' documentary series.
Dunbar was quickly commissioned to write a follow-up work, creating Rita, Sue and Bob Too, first performed in 1982. The play explored similar themes to The Arbor, in this case depicting the lives of two teenage girls who are both having an affair with the same married man. Dunbar's third play, Shirley (1986), placed greater emphasis on the central character.
The film version of Rita, Sue and Bob Too (1987) was adapted for the cinema by Dunbar and directed by Alan Clarke. The film created considerable controversy on the Buttershaw estate because of its negative portrayal of the area. Dunbar was threatened by several residents, but nevertheless stayed living on the estate.
Andrea Dunbar first became pregnant at age 15; the baby was stillborn at 6 months. She later had three children by three different fathers. The first, Lorraine, was born in 1979 to an Asian father. A year later, in 1980, Lisa was born, again while Andrea was still a teenager.
As a single mother, Dunbar spent 18 months in a Women's Aid refuge and became an increasingly heavy drinker. In 1990 she died of a brain haemorrhage at the age of 29 after becoming ill in the Beacon pub on Reevy Road. In 2007 her eldest daughter Lorraine, a heroin addict at the time, was convicted of manslaughter for causing the death of her child by gross neglect after the child ingested a lethal dose of methadone.
In 2000, Dunbar's life and her surroundings were revisited in the play A State Affair by Robin Soans.
A film about her life, The Arbor, directed by Clio Barnard, was released in 2010. The film uses actors lip-synching to interviews with Dunbar and her family, and concentrates on the strained relationship between Dunbar and her daughter Lorraine. The film was nominated for a BAFTA award for Outstanding Debut by a British Director, and won the Sutherland Trophy, at the 2010 London Film Festival Awards. It also won the Sheffield Innovation Award at the 2010 Sheffield Doc/Fest.
A novel inspired by Dunbar's life and work, Black Teeth and a Brilliant Smile, by Adelle Stripe, was published by Wrecking Ball Press in 2017.