A man has admitted crossing to the wrong side of the road to run down a cyclist with his car in a road rage incident in Perth.

Richard Sheridan, 54, struck cyclist Derek Holland on Beaufort Street near the Roe Street intersection in January.

The cyclist received minor injuries but described the incident as the scariest thing that had ever happened to him.

Mr Holland said it started when the driver cut him off, and he struck the car with his hand.

He said the driver then did a U-turn, crossed to the wrong side of the road and hit him, knocking him off his bike.

A nearby police officer dragged the driver out of the car and arrested him.

"It's very, very lucky that I didn't get more hurt than I have been today," Mr Holland said at the time.

"It was probably the most scariest thing that's ever happened to me."

In the Perth Magistrates Court today, Sheridan pleaded guilty to reckless driving and causing grievous bodily harm.

He is due to be sentenced next month.