Grand Central Savings, which operates branches in Glasgow and Greenock, is to open a series of "remote tellers" to provide savings accounts and other banking services in deprived communities.
The first, in Easthall Park, Easterhouse, will open tomorrow, with a second teller in Govan opening in November.
GCS is also in negotiation with Edinburgh City Council and seven housing associations to extend its services in the capital and expects to open a remote terminal in Alloa early next year.
Discussions are also taking place to bring the service to 13 other council areas, including Aberdeen, Dundee and North and South Lanarkshire.
The move offers marginalised people banking facilities without the photographic ID and other stringent requirements of high-street banks. Only an NI number is needed, or a Home Office registration card, plus one other type of ID.
Jackie Cropper, chief executive of GCS, said the new remote branch would expect to have around 250 customers in its first year, to add to the charity's existing 3500 clients.
Large numbers of Scots are unable to use traditional bank accounts for various reasons such as a bad credit history, lack of a fixed address, or having recently spent time in prison, she said.
"This is a first step for vulnerable and marginalised people who are virtually invisible. Without this service, they would be left to rely on payday loans companies and doorstep lenders," she said.
The first launches in Glasgow are in association with Easthall Park Housing Co-operative, Govan Housing Association, Elderpark Housing Association and Linthouse Housing Association, as part of a programme to offer welfare rights advice and money advice.
Easthall Park Housing Co-op director John McMorrow said: "We'll offer budgeting advice and welfare rights support. These are things they need but they may not have the necessary skills at the moment."