Darren Richmond put his foot down and purposely rammed a police vehicle that had been parked across a road to stop him.
Leeds Crown Court heard the 44-year-old stole the Mercedes Sprinter from The Chase, Stanley, Wakefield on the evening of February 22 this year.
Joseph Hudson, prosecuting, said Richmond then drove the van to the Beeston area of Leeds.
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Police officers became suspicious when they saw the van being driven at around 11pm being followed by a moped.
When he realised the police were following him, Richmond made a series of sharp turns.
Officers called for back-up and asked for a vehicle to block him in.
Mr Hudson said: "The defendant came to the block but rather than stop, he rammed into the police vehicle at speed, causing injury to a police constable who was sat in the passenger seat.
"He went past the block and drove off."
He was arrested and gave no comments during an interview.
The police officer was taken to hospital with whiplash and needed a week off work.
She gave a statement saying she "feared for her life" when saw the van accelerating towards her.
The officer described how she could have suffered greater injury had she not moved partially from her own seat onto the driver's side at the moment of impact.
Richmond admitted charges of dangerous driving, theft of a motor vehicle and driving without a licence and insurance.
Read more: Drunk homeowner spat in policewoman's face when officers were called to illegal lockdown garden party in SeacroftThe court was told Richmond has 18 convictions for 32 offences dating back to 1995, including multiple thefts, and dangerous driving in 1998 in which he banned from the road and ordered to take an extended test. He has never passed that test.
Shila Whitehead, mitigating, said Richmond, who has no fixed address, had stolen the van so he could sleep in the vehcile.
She said: "He has no family and was in a bad state at the time. He had nowhere to stay.
"He is deeply regretful for not stopping."
Judge Rodney Jameson QC jailed Richmond for 20 months and banned him from driving for 34 months.