This Excelsior-class starship was among the first of the four in the U.S.S. Saratoga's group at the Battle of Wolf 359 to be locked on by the Borg and put out of commission.

The enemy's cutting beam destroyed the port side of the Melbourne's primary hull and was one of 39 vessel casualties. In 2364, it was stationed at Starbase 74 and was in range when the Bynars hijacked the Galaxy-class Enterprise-D. However, the Melbourne could not respond due to maintenance adjustments in progress.

In late 2366, Commander William Riker was offered its command, but declined it, in favor of remaining as first officer on board Enterprise. The Melbourne was named for the Australian city on Earth.