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.
One of the UK's smaller energy suppliers has topped a list of the highest proportion of consumer complaints.