The contractor, who did not want to be named, was working at the junction of West Street and Lincoln Road (A158).
He said the incident happened on September 10 when temporary barriers were removed to allow staff and school buses access to Queen Elizabeth’s Grammar School on West Street.
Access is restricted to approved vehicles.
However, the contractor said a ‘four-wheel drive vehicle’ attempted to get through the barriers.
He revealed there was a male driver, a female front seat passenger and two children in the back.
He says when he attempted to stop the car, it drove straight at him, forcing him to ‘leap out of the way’.
The contractor said police were called, but he understood no action was taken because the incident was not recorded on camera.
Lincolnshire Police confirmed the incident had taken place.
A spokeswoman added: “The driver reportedly did not stop for the contractor but sped off almost hitting him. An allegation of dangerous driving was received.”
Police did not reveal any further details.