Npower's performance has been branded as "unacceptable" by a watchdog after it topped a complaints list among the major energy firms.
The company recorded 202 complaints per 100,000 customers in April to June - five times more than the best performing firm, SSE.
The figures, from watchdog Consumer Futures, cover a three-month period before the latest round of price rises.
Npower boss Paul Massara recently said his bonus was "linked to performance".
The chief executive dismissed giving up a bonus in response to anger over rising energy prices as a "gimmick".
In an interview with the BBC's Hardtalk, he said: "My bonus is linked to my performance, is linked to getting it right for customers, is linked to employee satisfaction. All of my team are linked to that. If we don't deliver on that, we don't get a bonus."
He said he earned about £600,000 a year, which included a £150,000 bonus.
Centrica boss Sam Laidlaw has pledged to decline a bonus this year to help restore trust in energy companies.
Consumer Futures said that energy firms still had "a long way to go" in improving complaints levels and consumer trust.
The data shows that between April and June, Npower's complaints levels were the highest, followed by EDF (75 complaints per 100,000 customers), then E.On (60 complaints per 100,000 customers), British Gas (55), Scottish Power (41), and then SSE (38).
"We know that some of our customers have not had the service they deserve," said Roger Hattam, director of domestic retail business at Npower.
"We've had some challenges with a new computer system and we are sorry that this has caused problems for customers. I want to reassure them that we are working very hard and making progress in ensuring that these issues are resolved as quickly as possible."
The watchdog accepted that there had been issues implementing the new system, but Npower's performance was still unacceptable.
"Companies must remember that many people view how a firm handles their complaint as a sign of how valued they are as a customer - so it is essential to deliver on this key issue," said Audrey Gallacher, director of energy at Consumer Futures.
On average, complaints levels grew over the spring months compared with previous months.
Gillian Guy, chief executive of Citizens Advice, said: "People are being hit with large back bills, find their bill unclear and direct debit customers are frustrated companies are holding on to their money when they are in credit."
Npower was the third major supplier to announce price rises for the winter, with a dual-fuel bill to go up 10.4%.
The price rise, which will take effect on 1 December, is the highest increase announced by any supplier so far.
However, it said it would cut its planned rise to 6% if the government reduced green levies.