Councillor Shaffaq Mohammed, leader of the party, sent a letter to Kwasi Kwarteng, secretary of state for energy, urging him to adopt a one-off levy which could raise more than £5 billion to support those struggling with sky-rocketing energy bills.
This could equate to thousands of families in Sheffield getting hundreds of pounds of support, he said.
He added: “It can’t be right that a few energy firms are making millions from record gas prices while people can’t even afford to heat their homes as the cost of living crisis hits Sheffield hard.
“A one-off Robin Hood tax on gas and oil bosses would provide vital funding to support families in our area who are facing crippling energy price hikes.
“For years the Conservatives have ignored this problem and failed to take the bold action we need to reduce fuel poverty. The Government cannot look the other way any longer while families struggle to get by.”
He said the money raised through this could fund a substantial package of emergency support including doubling the Warm Homes Discount and extending it to all those receiving Universal Credit or Pension Credit.
Coun Mohammed said this would give 62,896 households in Sheffield £300 each off their heating bills this year.
The party is also calling for the winter fuel allowance to be doubled, which it said would benefit 76,720 pensioners in the area.
Why are energy bills so high?
There has been a worldwide squeeze on gas and energy supplies and as a result, wholesale energy prices have increased sharply.
Various factors have played a part in this, including recent cold winters putting pressure on supplies, a relatively windless summer making it difficult to replenish supplies and increased demand from Asia for liquefied natural gas.
The UK has been hit relatively hard because it is one of Europe’s biggest users of natural gas – 85 percent of homes use gas central heating and it generates a third of the country’s electricity, while storage capacity in the UK is lower than some other European countries.