The weather in the Melbourne area was clear, with good visibility. Runway 34 was in use and visual approaches were required. The aircraft, which was approaching Melbourne Airport from the west, was radar vectored onto base leg and descended to 3000 feet. At 1704 hours Melbourne Approach Control advised the crew that their position was nine miles south-west of the field. They were asked to advise when they had the runway in sight and also to say when the runway 34 lead in strobe lights were sighted. Shortly after, the crew responded that they had the runway and strobe lights in sight. Approach Control gave the crew their position as six miles south-west of the field, told them to make a visual approach and not to descend below one thousand five hundred feet until established on final. At 1706 hours the controller told the crew they were approaching the runway extended centre line. The Approach Controller noted that the aircraft was passing through the extended centre line and had not turned to line up with runway 34. He promptly issued instructions to the aircraft to climb to 2000 feet. At about the same stage the crew realised that the runway they had been looking at was too short for their operations and also decided to go around. Further radar vectors were given and the aircraft subsequently landed normally on runway 34 at Melbourne without any other problems. Runway 35 at Essendon Airport was the runway sighted by the pilots. It does not have lead in strobe lights. The crew indicated they must have seen reflections near Essendon which they mistook for strobe lights. On the approach the crew had seen a runway from a long way out, which they thought was the north/south runway for Melbourne Airport, but was in fact runway 35 at Essendon Airport. In the lighting conditions at the time they did not see Melbourne Airport, until on the go around. Runway 34 at Melbourne does not have an instrument approach procedure. However, the 165 radial from the Melbourne VHF Omni Range (VOR) radio aid at Melbourne Airport can be used to give an indication of the extended centre line for runway 34. Distance information from Melbourne was also available from the Melbourne International Distance Measuring Equipment. On the approach the minimum height descended to was just over 1000 feet above the elevation of Essendon Airport.