Redcap School, in the Broomy Hill area, was founded in 1923 and was taken over by the Haberdashers' Company of Schools in 2004.
Despite being told that its standard of teaching was "outstanding" during an Ofsted inspection in March, the primary school is not attracting enough pupils.
Parents have been informed of the decision to close the site, which is expected to be sold.
In a statement, the school said fewer children were being born in the county and a number of primary schools in the state sector had found it increasingly difficult to keep pupil numbers up.
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