Co-operative Energy received 136 complaints per 100,000 customers in the third quarter of the year, the Energy Ombudsman said.
This was 50% higher than any other supplier, the ombudsman's figures show.
Co-operative Energy blamed continuing problems with its new computer system for the results.
It upgraded its IT systems in March, with many customers complaining of being locked out of their online account or not receiving their bills following the switch.
"We would like to thank customers for their patience and continued support in recent months," a spokesman for the supplier said.
"We have made significant progress to resolve a number of technical issues which ultimately related to the introduction of a new IT system. We will continue to make further improvements to ensure our customers receive the high level of service they expect and deserve."
The energy ombudsman said it had received a total of 13,212 complaints about the energy sector in the third quarter of the year, slightly lower than the previous quarter's total of 13,490.  Disputed charges, inaccurate invoices and missing bills were the most common complaints.

The 23-year-old carded a final-round five-under-par 67 to finish on 11 under at the Trump National in New Jersey.
Compatriot Choi Hye-Jin was two strokes behind in second, while China's Shanshan Feng, who held a one-shot lead overnight, went round in 75 to finish tied for fourth, five strokes adrift.
A South Korean has won the US Open seven times in the past 10 years.
Park told Fox Sports: "I did not have the best first and second rounds so I wanted to believe in myself in the remaining rounds. Trusting myself definitely helped."
England's Charley Hull finished 11 strokes behind Park on level par, with Scotland's Catriona Matthew a further six shots back.

Nearly half the roughly four million children displaced in the region are not in school, according to a new report by the Malala Fund.
They risk becoming a "lost generation", Ms Yousafzai warned.
The BBC's Lyse Doucet was given exclusive access to the report ahead of its release on Friday.
Ms Yousafzai, who was shot in the head by the Taliban after campaigning for education for girls in Pakistan, has been raising awareness of the lack of education for Syrian refugees.
A growing number of Syrian girls are already teenage brides, or working in farms and factories, our chief international correspondent reports from the Jordanian capital, Amman.
Major donors are under pressure from Syria's neighbouring countries to provide substantial long-term support if they wish to convince Syrian families to stay in the region instead of heading to Europe.
"It's time for the world to match their commitment to get every Syrian child back in school," Malala Yousafzai told me in an email.
The 18 year-old campaigner for children's rights will be attending the London Conference with 17-year-old Syrian education activist Muzoon Almellehan, whose family recently settled in the UK.
"My generation is not lost," she insists.
But the longer Syrian children stay out school, the greater the risk they will not return.
British officials say it is not a realistic goal to get them back in class by the end of the next academic year. But they are still pushing hard.
UK International Development Secretary Justine Greening told me: "We must ensure Syria's children do not become a lost generation."
According to the report by Ms Yousafzai's's charitable fund, donors have provided only 37% of the money needed to supply resources such as school places and teachers.
It says $1.4bn (Â£1bn) a year is urgently needed to plug the gap.
Ms Yousafzai has warned that children are being deprived of education at a time when they begin to form into future doctors, teachers, and engineers.
The report comes ahead of next week's Syria Conference in London, where donors will be asked to pledge that all Syrian refugee children in the region should be in school by the end of the next academic year.
But even Nordic countries, which have been taking the lead on funding, are indicating that they may need to divert money to educate Syrians arriving in their countries.
According to Ms Yousafzai, neighbouring countries are already bearing too much of the cost of educating Syrian refugees.
One of the UK's smaller energy suppliers has topped a list of the highest proportion of consumer complaints.
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South Korea's Park Sung-hyun won the US Women's Open by two shots to claim her first LPGA title in her debut season.
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Campaigner Malala Yousafzai has called for more to be done to educate millions of Syrian refugee children displaced within the country and its neighbours.