The man was pronounced dead at the scene of the crash on the A350 at Longbridge Deverill near Warminster at about 16:15 GMT on Saturday.
Wiltshire Police want to trace the driver of a blue car which was travelling behind the moped.
The road was closed in both directions for several hours. Police are appealing for witnesses to the incident.
A 20-year-old man died when his moped was involved in a head-on collision with a van in Wiltshire.