Officers were called at 12.45am, on December 3, to reports of a crash between a car and a pedestrian on Locks Road.
A 33-year-old man was walking with friends when the incident happened.
He suffered injuries to his forehead, leg and shoulder and was taken to Queen Alexandra Hospital, in Cosham, for treatment.
The vehicle, believed to be red, failed to stop.
Police would like to speak to any witnesses who saw the car or anyone who thinks they may know the driver involved.
Anyone with information should call police on 101, quoting 44170469299.