The lawyer for a Perth driver who ran down a cyclist has told the Perth Magistrates Court his client is mortified about the uncharacteristic "overreaction".

Richard Sheridan, 54, admitted crossing to the wrong side of Beaufort Street in January of this year and striking cyclist Derek Holland with his car.

The cyclist was left with multiple fractures and grazes on his arms, legs and torso.

The Perth Magistrates Court was told the early morning incident started with a minor disagreement and escalated when the cyclist hit the driver's windscreen, causing it to crack.

The court heard that "enraged" Sheridan, who spun his car around and accelerated heavily.

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

It happened outside the police complex on Beaufort Street, near the Roe Street intersection, and several police officers were on the scene in seconds.

They arrested Sheridan and he was charged with reckless driving and causing bodily harm.

Sheridan pleaded guilty to the charges last month and on Tuesday his lawyer Curt Hoffman said his client did a "profoundly stupid" thing and his "greatest error" was following the cyclist.

Mr Hoffman told the court Sheridan, who is an architect, does a lot of community work and is a former chair of homeless organisation Shelter WA.

Magistrate Elizabeth Woods described the incident as a "brain snap", and cited a report provided to the court in which Sheridan said he was not a morning person.

"I'm not a morning person either but I don't go hitting people on bicycles," she said.

Sheridan is expected to be sentenced on Thursday.

The court heard he has already paid more than $6,000 to replace the victim's bicycle.