Melanie Dolby, 48, from Sherwood Rise, Nottingham, was knocked down near a party taking place in Radford in June. A man, 52, sustained serious injuries.
Johan Martin, 20, admitted causing death and serious injury by dangerous driving.
Martin, along with another man, had originally been charged with murder.
The case against Jamal Rodney was discontinued in November.
Martin, of Vernon Road, Nottingham, was sentenced at Birmingham Crown Court. He was given a further term of three years' detention for causing serious injury, to run concurrently.
He was also banned from driving for seven-and-a-half years.
Nottinghamshire Police said Martin only had a provisional driving licence when the Ford Mondeo he was driving struck Melanie Dolby, causing her to become trapped under the vehicle.
Her friend Leroy Taylor sustained serious injuries in the crash but has since made a full recovery.
Police said Ms Dolby had been walking to a party at Moog Bar in Gamble Street at the time of the incident.
Martin had driven to the party in the Mondeo, which was owned by his friend.
Det Ch Insp Rob Severn said: "Johan Martin was not qualified to drive the car and had a complete disregard for anyone else in his path as he reversed at speed away from the party.
"As a result of his actions Ms Dolby was struck by the car and subsequently lost her life."
He added: "The sentence will not be of any consolation to Melanie's family and friends who have lost someone who was clearly much loved. Our thoughts go out to them at this time."
An unqualified driver who reversed at speed killing a pedestrian and seriously injuring another has been detained for five years.