It is designed to appeal to those who are put off by unexpected penalties levied in certain instances for missed payments, which cost some customers £140 a year.
The Control Account is one of three current accounts being launched by the Post Office - in partnership with Bank of Ireland - in a pilot across 29 branches across East Anglia, as it seeks to beef up its presence on the high street as a major financial services provider. A full launch across the network is planned for 2014.
Control Account customers will be asked to pay £5 a month to ensure that they do not face further banking charges when payments are returned unpaid for direct debits and standing orders. The minimum deposit is £20.
Many of those who do not have bank accounts are thought to be deterred by the risk of such penalties, but as a result can miss out on better deals for utility payments.
The Post Office said paying such bills by direct debit could save customers on average £125 to £215 a year.
It is also offering a Standard Account billed as its "free in credit" everyday bank offering as well as a Packaged Account which offers added benefits such as travel insurance and breakdown cover for an additional £8 a month.
The Post Office initially announced last month that it was moving into the current account market but without giving details. The new products could make it easier for those in rural communities to access their money, as 99.7% of people live within three miles of a branch.
Nick Kennett, director of financial services, said the range of accounts would offer a greater choice to customers and a "fair and transparent" way to manage their money.