Npower will provide vouchers worth up to Â£49 to people referred to Gloucester Foodbank who use pre-payment meters.
It said that would keep their lights and heating on for up to two weeks.
The latest statistics suggest that there were 2.35m households in fuel poverty in England in 2013, about 10.4% of households.
The pilot scheme is designed around the food bank service, which provides free food to people in acute need, usually after a referral from a doctor, social worker, or Jobcentre staff.
Npower customers with pre-payment meters who are referred to Gloucester Foodbank, on Great Western Road, can apply for a credit to top up their meter. Those using other energy firms considered "most in need" by food bank managers could also be eligible.
The aim is to stop people deliberately going without gas and electricity to save money.
The Npower scheme is the first in south-west England, although it has also started four trials in Kingston-Upon-Thames, London, and 16 in County Durham.
It is being run in partnership with charities the Trussell Trust and National Energy Action.
The way food poverty in England is measured has changed: households are now considered to be in fuel poverty if, once they have paid essential energy bills, they are left with income below the official poverty line.
The government says the fuel poverty "gap" - which measures how much the poorest need to spend on bills, compared to typical households - is narrowing, because of rising incomes and energy-efficiency measures.
Vouchers for electricity and gas will be given to people considered most in need as part of a "fuel bank" trial in Gloucester.