A statement from the bank says: "We have taken the difficult decision to close the NatWest Llangollen branch on the 21st September 2015.
"We are working hard to ensure there are a number of alternative ways for people in the area to continue to bank with us.
"We have reached an agreement with the local Post Office, which is 0.1 miles away from the branch so that our customers can check their balance, deposit and withdraw funds, and business customers can get coinage.
"We will keep the ATM in the local community, and there are also 4 other free to use ATMs within 1 mile of the branch.
"We are introducing a mobile branch service to the community and we will be engaging with our customers and the local community to understand the best day and time for the mobile branch to visit.
"The number of transactions taking place at NatWest Llangollen branch has dropped by 38% since 2011 and only 35 customers use the branch on a regular weekly basis. Sixteen of these customers already use other branches in the area.
"We are committed to following the UK Government protocol on branch closures, and we have made the decision following careful consideration of a wide range of factors including branch usage and the alternative ways our customers can bank with us locally.
"Our customers are increasingly using alternative ways to bank with them such as online and mobile banking. As a result, branch transactions have declined by around 36% since 2010 whilst online and mobile transactions have grown by more than 300%. Only 9% of their total transactions are now undertaken in branches in comparison to 25% in 2010.
"We are writing to all of our customers who use the branch, as well as displaying posters in branch to let them know of the closure. Between now and the closure date, we will engage with all of our customers, local businesses and the wider local community to make sure they are aware of the alternative ways of accessing their banking with us in the local area, and to answer any questions they might have."
The announcement has caused anger amongst local politicians.
Clwyd South Assembly Member Ken Skates, who has his office in Llangollen, said: “I am bitterly disappointed by this decision and will be seeking an urgent meeting with NatWest.
“I am a NatWest customer myself and this will mean people will have to go to Wrexham for a face-to-face service, which remains particularly important to many. It’s not even in the same county and it’s simply too far to travel for some.
“Loyal customers haven’t even been consulted about this and many will find out that their branch is closing through the local press, so NatWest shouldn’t be surprised if people show the company the same disregard and opt to take their money elsewhere.”
He added: “If these closures are pushed through, I will demand assurances that the mobile unit mentioned by NatWest will visit Llangollen several times a week and that all customers will be fully informed about when it will be available.”
Local county councillor Stuart Davies said: "I am deeply disappointed to hear this news.
"All banks should remember that with the right to make a profit comes responsibility to communities such as Llangollen.
"This closure will cause particular difficulties for the large number of businesses in the town plus local clubs and societies who have cash and cheques to bank.
"These will now have to be taken to other branches, leading to major inconvenience and security problems."
As yet there has been no confirmation of the move by NatWest.