Wiltshire Police said it happened just before 1800 BST on Wednesday at the junction with High Street in Codford.
The motorbike was travelling south towards Salisbury when it was in collision with the car, police said.
The motorcycle rider was a 49-year-old man and the car driver was a 61-year-old man. Both were local, and were pronounced dead at the scene.
The road was closed for six hours while police carried out an investigation.
A motorcyclist and a car driver have been killed in a crash on the A36 near Warminster.