Homemart, which sells food and household goods, opened on Kirkgate in November in a unit previously run by clothes retailer Edinburgh Woollen Mill.
Homemart's bosses insisted they would "not contribute" to Kirkgate's well documented problems with anti-social behaviour and argued their stock was no different to that of a small Tesco or Sainsbury's.
But a council committee concluded that granting a licence could cause "further public nuisance".
Homemart has now submitted a second application, asking for permission to sell alcohol between 9am and 10pm every day of the week.
Members of the public can submit comments on the application to the council, before a deadline of January 10.
Local Democracy Reporting Service