A court was told Mohammed Fike Butt carried out the killing and attempted to murder two other men to "teach them a lesson."
Butt has gone on trial at Leeds Crown Court accused of murdering Jason Llanwarne on North Street, Headingley, on September 14 last year.
The 31-year-old defendant is also accused of the attempted murder of Dean Ward and Scott Chalders during the same incident.
Outlining the case, Stephen Wood QC, prosecuting, told jurors how Butt used his Mazda vehicle "as a weapon."
He said: "He struck one of those males but nevertheless carried on driving.
"He then turned the car around, mounted the pavement again and drove once more at speed at the same group."
"This time an additional male was on the pavement.
"The prosecution say that the defendant's intention was to kill each of these three males."
Mr Wood said the third male was struck by the Mazda and thrown onto the bonnet before falling off, suffering fatal injuries.
The prosecutor continued: "The force of that impact between this male and the windscreen was such as to shatter the windscreen of the defendant's car, making it quite impossible to see through.
"You may think that in those circumstances it was unsafe, and indeed dangerous, to drive a car in that condition.
"But, ladies and gentlemen, having struck this male in what was an obvious heavy collision, the defendant nevertheless carried on driving.
"He left the pavement and went back onto the carriageway.
"He turned around and mounted the pavement before driving towards the body of the male on the pavement.
"Quite deliberately, we suggest, he drove his vehicle over the body of that male."
Mr Wood said one witness described the incident "as if the defendant was driving over a speed bump."
The court heard CCTV footage recovered after the incident showed Butt with his head out of the driver's side window in order to get a clearer view.
Mr Wood said the defendant then drove off, abandoned the vehicle and went to buy chips from a takeaway.
He added: "At no stage did he demonstrate any regard for the well-being of the three males.
"The prosecution say this was all about teaching these three males a lesson.
"It was a lesson which was to cost (Mr Llanwarne) his life."
Butt, of Cross Flatts Avenue, Beeston, pleads not guilty to murder, two counts of attempted murder and dangerous driving.
The prosecution's opening of the case will continue at 2pm today.