The increase will add an additional £39 to the bills of customers on its iSave Everyday tariff from the start of April.
The supplier said £7 of the increase was due to increased wholesale costs, £19 was due to higher transmission and distribution costs, and £13 was due to additional costs paid to the government to support renewable energy.
The typical bill will now increase from £1,124 a year to £1,163 a year.
First Utility said that less than 40 per cent of its customers would be affected by the price increase as the majority of its customer base has fixed term deals.
The supplier said it also faced an additional cost of £23 per customer in 2014 to meet its Energy Company Obligation, but these costs will be absorbed by the company rather than passed onto consumers.
First Utility also confirmed it would credit all electricity customers with the £12 rebate from the revised Warm Homes Discount Scheme in the autumn.
Ian McCaig, chief executive at First Utility, said: “Our mantra is to help consumers minimise their energy spend by offering lower tariffs and campaigning for change in the industry to reduce costs and put more power in the hands of the consumer.
“Unfortunately we’re in an industry where costs are continuing to rise – driven by investments in infrastructure, policy costs and a gradual increase in wholesale costs.
“However, we’ve held off making any increases during the winter when usage and therefore bills are at their highest and we have absorbed increasing costs as much as we can – that’s why our increase is lower than the big six.”