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.

They will meet on Monday afternoon to decide their response.
The boss of the bank has described this plan as getting "several holes in one in a row".
Golfers will know how hard that is and the wind of political risk has just picked up.
If they do decide the plan is now too risky then the government may have no choice but to nationalise the bank.
That would trigger a so-called "bail in" which means people who lent the bank money would have to write it off.
Unfortunately, 65% of those creditors are ordinary retail investors so the damage would be widespread and politically toxic.
There is another option.
The Italian government could decide to simply break the rules and nationalise the bank without hitting small investors.
That might be politically expedient but would be bitterly opposed in Germany and would set back immeasurably the project of banking union (separating the financial risk of banks from their governments - a move that came in response to the eurozone crisis of 2012).
The money comes directly out of some small investors' pockets or it comes out of every citizen's taxes.
The latter would be seen across Europe as a massive defeat in the battle to make sure taxpayers are not the first port of call when a bank fails.
The fate of Europe's oldest and weakest bank has ramifications not just for Italy but for the entire European banking reform project.

He said at an industry event that Britain's largest carmaker by volume would like to double production from 500,000 to one million cars a year.
But it would depend on the government helping to upgrade power supplies and invest in surrounding infrastructure.
The firm would also like a guarantee on access to engineering talent.
A company spokesman said the production target was "very much a want, rather than a will", but declined to commit on precise job numbers.
The 10,000 figure was mentioned by Lord Kumar Bhattacharyya, chairman of Warwick Manufacturing Group, which is part of Warwick University. Although it was not confirmed by the company, it was not dismissed either.
The carmaker's vision comes after the decision of Nissan to move two new next generation models to its Sunderland plant, backed by assurances from the government that it would help to invest in automotive research and development.
Nissan produced almost 477,000 vehicles in the UK last year, while just under 490,000 rolled off Jaguar Land Rover's (JLR) production lines, according to industry body the SMMT.
Now it seems JLR has thrown down the gauntlet to the government to match its ambition with big pledges for investment.
Specifically, the company is looking for help with infrastructure surrounding a 60 acre site and provide significant additional power resources.
Lord Bhattacharyya said he was sure "more than 10,000 jobs" would be created if JLR expanded to manufacture electric vehicles and batteries in Coventry.
He said the Business Secretary, Greg Clark, gave his assurances the government would look at the plans very seriously, because "in order to make the batteries and cars we need the power supply, which there is a shortage of in this area".
"There are challenges, but Coventry and Warwickshire is well placed to help make it happen, and I believe the timing is right," agreed Jonathan Browning, chairman of the region's Local Enterprise Partnership.
It is a tantalising vision of huge investment in the automotive heart of Britain.
Can the government match the soaring ambition of one of the UK's largest manufacturers with similarly ambitious support?
Although the company described this as an aspiration more than a plan, it is much more than day-dreaming.
According to company sources, this vision has been long held by JLR's boss, but he had chosen not to share it before and the Business Secretary was in the room to hear it.
The message was clear - the ball is now in the government's court.
Up to 47 jobs are at risk after a Grimsby shop confirmed it is to close after nearly 70 years of trading.
[NEXT_CONCEPT]
Although the share price of Europe's oldest bank Monte dei Paschi is little changed this morning, that may not last if the consortium of investors planning a â‚¬5bn cash injection abandon their rescue attempt amid the political vacuum opened up by Italian Prime Minister Matteo Renzi's departure.
[NEXT_CONCEPT]
Jaguar Land Rover's chief executive Dr Ralf Speth has laid out a future vision which could see 10,000 new jobs created in the West Midlands.