VH-TJH was departing from runway 27. The clearance was for a radar one departure, initial heading 270 degrees and a requirement to maintain an altitude of 3000 feet. After take off the crew called on Melbourne departure control frequency at 2029.51, stating they were turning right onto 270 degrees, climbing to 3000 feet and passing 2000 feet. In response they were told they were identified. A short time later, at 2030.55 they were told to turn right onto a heading of 310 degrees to intercept the 285 radial from the Melbourne VOR. At 2032.25 the crew of VH-TJH told the departures controller they required an immediate climb. The controller immediately cleared them to climb from 3000 feet to flight level 350. The aircraft track had taken the aircraft towards rapidly rising terrain west-north-west of Melbourne. The higher points along this track are between two and three thousand feet. The aircraft Ground Proximity Warning System operated to give a warning of 'Terrain, pull up.' The crew responded by quickly commencing a climb, and this caused the GPWS to cease operating. At that time of night, due to decreased traffic conditions, the approach and departures air traffic control positions were combined so that they could be operated by one controller. This also included the radar advisory service, (RAS). For the departure of VH-TJH the controller put an altitude restriction on the aircraft due to an aircraft inbound from the west. Other traffic was handled during this period and a call on the RAS frequency also occurred. A further call was received from Moorabbin Tower to arrange a clearance for an aircraft taxying at Moorabbin. The situation regarding the aircraft approaching from the west was resolved by the time VH-TJH first called after becoming airborne. The altitude restriction of 3000 feet could have been removed then but was overlooked. While handling other matters the contoller omitted to remove the restriction as the aircraft tracked outbound towards rising terrain. The GPWS warning was genuine. The crew of VH-TJH did not take any early action to request a climb despite the fact they were tracking towards rising terrain while maintaining 3000 feet. Significant Factors The following factors were considered relevant to the development of the incident: 1. The Controller omitted to remove the altitude restriction placed on VH-TJH, in a timely manner. The precise reasons for this happening could not be determined. 2. While tracking towards rising terrain at an altitude of 3000 feet, the crew of VH-TJH took no action to request a climb prior to activation of a GPWS alert.