Mothercare is set to close 60 UK stores by June next year, affecting 900 jobs.
The Brighton store, in Churchill Square shopping centre, is among those to close.
It announced in May it would shut 50 stores, but has now said a further 10 will also close.
The Worthing store closed last year. Eastbourne looks to be among the 77 set to remain open.
Clive Whiley, interim executive chairman of Mothercare plc, said when he joined the company three months ago Mothercare ‘faced a bleak future with growing and pressing financial stresses upon the business’.
But he said the restructuring of the company would ‘get Mothercare back to where it should be as a fit for purpose business’.
Other companies which have closed stores in the city this year include Maplin in Brighton and Toys R Us in Hove.