Olaitan Roberts was last seen at near to Langley Green hospital in Martyrs Avenue at around 5.30pm on Sunday (July 9).
The 20-year-old is 5ft 9in, with very short cropped black hair.
He was last seen wearing a maroon hooded top, dark blue jeans with holes and trainers.
Officers are growing increasingly concerned due to a recent deterioration in his mental health.
Olaitan has links to Worthing, Lancing, Crawley and Croydon.
Anyone who has seen him is asked to contact police online or 999 in an emergency quoting serial 1480 of 09/07.