Police officers were called to Queensway shortly after 2.20pm on Wednesday (December 22), after a collision involving a car and a bicycle.
It involved a silver Audi A3 and a cyclist near the parade of shops, Sussex Police said.
A man, aged 20, suffered serious injuries and was taken to hospital as a result of the collision.
Police said a 19-year-old man, who was driving the Audi, was uninjured.
Police have now launched an appeal for witnesses.
A spokesperson said: "Anyone who saw what happened or who has relevant dascham or CCTV footage is asked to contact us via email: [email protected] via the Sussex Police website or call 101 and quote serial 719 of 22/12."