Terms and conditions of energy tariffs need to be more transparent to prevent people from getting a nasty surprise when their bills arrive, Consumer Focus said.
The consumer watchdog has written to the Office of the Gas and Electricity Markets (Ofgem), requesting an investigation into the way energy suppliers market and sell energy tariffs.
"We believe that energy tariffs are often structured in ways that are overly complex and can seem designed to confuse the average consumer," Audrey Gallacher, head of energy at Consumer Focus said in a letter to Ofgem.
"There are problems with dubious discounts that are hard to achieve. There are issues with the transparency of price rise notifications, termination charges and rollover contracts."
Ms Gallacher said the requested investigation would need to examine whether the average consumer was capable of understanding key terms and conditions of energy tariffs.
Quantitative research by Consumer Focus in March found more than one third of consumers were baffled by their energy bills.
"Nearly 60% of gas and electricity consumers did not know what tariff they were on or how much they paid per unit," Ms Gallacher added.
"When a household chooses the wrong energy tariff it can result in substantially increased annual bills."
Christine McGourty, director of Energy UK, said: "In our competitive energy market customers can choose from a wide range of different energy tariffs to suit their needs, and that is a good thing. Energy companies are constantly innovating to offer their customers a range of deals and a variety of payment methods.
"If people are unsure of being on the right deal they can call their energy company direct, who will be able to talk them through the best tariff available for them."