It is preferred bidder for Cleethorpes Academy and will start work on the £7.7m project in June to complete in September the following year.
Clugston will deliver a two-storey teaching block for 19 classrooms within the confines of the existing teaching blocks which will be refurbished while the school remains is use.
The showpiece of the new academy will be a sports block with a four-court sports hall, a gymnasium and fitness suite.
Steve Radcliffe, managing director of Clugston Construction, said: “With our design team partners Mabers and Ramboll, we are delighted to have been selected by the Academy following stiff competition through the National Partnerships for Schools Framework.
“Members of our staff attended the school before it gained academy status and others have children who will benefit from the new scheme, as future students.”