The Ramsdens Discount Department Store on Cleethorpe Road was opened in 1946.
The company said there would be some redundancies, but added it hoped "to be able to offer alternative employment to some employees".
Last year planning permission was granted by North East Lincolnshire Council to redevelop the site into a new retail park.
The store is expected to close over the summer.
In a statement, the firm's directors said the store had "continued to decline in what has become a very tough and competitive local market".
It added its nearby Home Interiors store would continue to trade.
Up to 47 jobs are at risk after a Grimsby shop confirmed it is to close after nearly 70 years of trading.