The big suppliers received a total of 1.7 million complaints in the first quarter, up from 1.48 million in the same period last year, consumer group Which? said.
Npower received 83 complaints for every 1000 customers in the first quarter of this year, the highest number among the six companies and up from 49 complaints per 1000 at the same time last year.
ScottishPower received the fewest, at 13 for every 1000 customers.
SSE, British Gas and E.On all received about 30 complaints per 1000 customers, with SSE's figures rising from 13 to 27 complaints per 1000 for the same time last year. EDF's complaints dropped from 77 per 1000 this time last year to 46.
The companies have published complaint figures since October 2012. In February this year Which? said the Big Six received more than 5.5 million complaints between January 1 and December 31 last year.
Which? executive director Richard Lloyd said: "Yet again millions of customers are being let down by poor service from the Big Six energy companies."
An Energy UK spokesman said: "Most customers are happy with their provider. But, in an industry which serves 27 million households, things can go wrong. Most issues just take just a call to fix even though all problems are lumped together. But all problems, no matter how minor, are important."