John Henderson ran over Audrey Gray in McGregor Street, Glasgow, shortly after he had been to a Rangers match on May 4 last year.
A senior judge told Henderson at the High Court in Edinburgh: "I don't think I can do other than impose a custodial sentence."
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At his trial Henderson was found guilty of causing the death of Miss Gray, 50, of Aboyne Street, Glasgow, by driving dangerously by causing the vehicle to collide with her and driving over her.
Henderson had claimed that the car lurched forward after his foot slipped off the clutch while he was adjusting his seat. The trial also heard that Miss Grey had been seen shouting at the car shortly before the fatal incident in the Drumoyne area.
The Lord Justice Clerk, Lord Carloway, said: "I take into account the fact that you are a first offender and I accept also you are a hard-working person who before this event led a blameless life. I also take into account the conduct of the deceased which was undoubtedly reprehensible in the manner she approached your car."
But Lord Carloway said he had to sentence on the verdict of the jury, and pointed out that causing death by dangerous driving was a serious offence.
Henderson, 55, of Holmpark, Bishopton, Renfrewshire, was also banned from driving for five years.