Grievances by consumers jumped by 23% to 65,168 last year, compared to 52,937 in 2014, said the independent adjudicator of disputes between the industry and its customers.
It said billing continued to be the most common problem, accounting for 83% of complaints in 2015. Late and inaccurate domestic bills were perennial issues.
Customers who had problems switching either suppliers or tariffs accounted for 9% of grievances.
Chief ombudsman Lewis Shand Smith said: "Energy complaints rose by nearly a quarter over the course of last year as customers continue to be more vocal about their discontent with suppliers."
One bright spot in the data showed complaints in the final three months of the year fell by 29% to 10,896, compared to 15,370 in the same period of 2014.
The chief ombudsman added: "Towards the end of the year, we've seen some suppliers take some encouraging steps, particularly when it comes to improving their billing processes, but there's still more that can be done.
"We encourage anyone experiencing an ongoing issue to speak to us - be it for advice or resolution, we're here to help and our complaints process is easy to use and free to consumers."
Annual breakdowns of complaints by firms will be made available next month by the Energy Ombudsman.
However, in the third quarter of last year, the body said ScottishPower received the most complaints, totalling 4,554, up 27% from the previous quarter.
Npower came second with complaints rising by 24% to 3,581, while British Gas was third with 1,305 complaints, a 1% fall on the second quarter of last year.
The Energy Ombudsman investigates serious complaints between customers and suppliers, where both sides have been in dispute for more than eight weeks and have reached deadlock.