It is the third fatal on this stretch of the A37 in nine months.
A Peugeot 206 was travelling southbound out of Bristol shortly after midday yesterday when it mounted the kerb before re-joining the road and then shortly afterwards left the road and hit a tree, which caused the car to roll and land on its side.
The driver received treatment at the scene from paramedics but died shortly afterwards.
Collision investigators closed the road for a time to enable an examination of the scene.
An Avon & Somerset police spokesman said: “We are keen to hear from anyone who was in Hursley Hill area at the time of the incident who may have information to help our inquiries.
“Anyone able to help is asked to contact the collision investigation unit on the force number 101, quoting reference CI/113/15.”