The scheme, which will be completed using a night road closure, will involve carriageway patching, repair work and lining.
The bridge will be closed going into Weston on Tuesday 4 and Wednesday 5 May between 8pm and 6am. The road will be closed going out of Weston on Friday 7 May between 8pm and 6am.
There will be no closure on Thursday 6 May due to the election.
A diversion route will be in place. Drivers will be asked to use the A370 (Herluin Way, Marchfields Way, Winterstoke Road), B3440 (Drove Road, Locking Road, New Bristol Road, Bristol Road), A370 Somerset Avenue and vice versa.
Cllr Mike Solomon, North Somerset Council's executive member with responsibility for roads said: "The A370 is a key route in and out of Weston and as a result Flowerdown Bridge is subjected to extensive wear and tear every day.
"This scheme will prolong the life of the road and provide a smoother carriageway for road users.
"We appreciate that the night closure will cause some inconvenience but have chosen to do this when traffic volumes are lower. We would urge people to be patient."
For more information visit www.n-somerset.gov.uk/roadworks