The suspect was identified as 28-year-old Marcos Gonzales.
The officer had pulled him over for not wearing a seat belt in the 13000 block of Brookhurst Street Wednesday morning.
At one point, Gonzales was able to get back in his car. He backed over the officer during his escape.
Gonzalez was described as 5 feet, 8 inches tall, 220 pounds, with a soft cast on his leg. He was driving a green 2002 four-door Infiniti Q35 with tinted windows.
As of Thursday, the officer remains in the hospital in good condition. He suffered moderate injuries including abrasions and bruises.
Anyone with information is urged to call the Garden Grove Police Department at (714) 741-5800.