The firm will carry out the second stage of works to expand Kingsgate Primary school in West Hampstead.
The project includes the construction of a new two-storey building for students aged four to seven years old, creating 420 places.
In addition, a new nursery will be developed along with a community centre.
The development is being funded by new residential and business space development on the same site, through Camden Council's CIP.
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The land for these elements will be sold by the Council, with planning consent, following completion of the school works.
Phase two of the project is expected to be complete at the end of next year to allow the new facilitiy to be open for the beginning of the new school year.
The first phase of works involved the site preparation and construction of the new school buildings, access road and landscaping required for the expansion.
Graham will also deliver enabling works including demolition of existing industrial units, construction of a retaining wall, and tree removal.
Project Manager Lead, Julie Crossen, Sweett Group, said: "We are pleased to have GRAHAM Construction as part of the project team to deliver Kingsgate Primary School in North West London.
"We look forward to working closely with them to successfully deliver this extension project for the London Borough of Camden in time for the beginning of the new school year in 2016."
(LM/CD)
