Scarborough's St Augustine's RC School is making a bid for £1.2m to North Yorkshire County Council's education authority, to build a teaching and science block.
Headteacher Roger Cannon said it was part of a long-term project to increase the number of students by 50 per cent.
The school became a regional Catholic school last year and takes students from an area stretching from Whitby south to Bridlington and inland to Pickering.
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