A 54-year-old driver who chased down and knocked over a cyclist on a Perth street has avoided an immediate jail term.

Perth architect Richard Sheridan ran a red light and crossed onto the wrong side of Beaufort Street in January and hit cyclist Derek Holland with his car.

Mr Holland was left with multiple fractures and grazes on his arms, legs and torso.

The incident started with a minor disagreement and escalated when the cyclist hit the driver's windscreen causing it to crack.

This enraged Sheridan who then did a U-turn and accelerated heavily.

The impact of the crash buckled Mr Holland's bike and he was dragged some distance underneath the car before it came to a stop.

Sheridan pleaded guilty to both reckless driving and an act or omission causing bodily harm.

His lawyer said his client was mortified about the uncharacteristic "overreaction".

In sentencing, Magistrate Elizabeth Woods said she accepted Sheridan's remorse and that he "didn't intend to chase and run him over".

But she warned that drivers needed to be respectful.

"People need to respect other road users," she said.

"The contact was significant. The injuries fortunately for the cyclist were not as bad as they could have been."

Ms Woods also cited references which described Sheridan as a "considerate person, who contributes to the community in a number of ways".

Sheridan was handed a nine-month jail sentence, suspended for nine months, and his licence was disqualified for a year.

He was also fined $1,500 on top of the $6,000 he paid the cyclist for the damage to the bike.