The scheme will see a full programme of maintenance works carried out overnight between 8pm and 6am for five nights, starting on Monday 2 August.
The road will be closed between the junctions with the A4174 Colliters Way and B3130 Clevedon Road so crews can work safely.
Works taking place will include gully emptying, grass cutting, tree clearance, lining and signage replacement.
A diversion route will be in place as there will be no access to Bristol via the A370 while these night-time works are carried out.
Cllr Mike Solomon, North Somerset Council's Executive Member for Neighbourhoods and Community Services, said: “This is a busy route in and out of North Somerset and closing it overnight will allow us to carry out important works to improve the route.
“We’ll be using the closure to carry out various essential maintenance works at the same time, therefore making the most effective use of the road closure."
“We appreciate that a night closure on a busy route will cause some inconvenience, but we carry out works overnight when traffic volumes are lower, to minimise disruption and avoid peak travel times.”
The cost of the works is £56,000.