Council tax is raised by local authorities across the country
Council Tax should be supplemented by a local income tax to make councils in England less dependent on central government for their funding, MPs say.
The Communitees and Local Government committee says radical reform is needed to correct the imbalance of power between central and local government.
Currently 75% of funding for councils in England comes from the government.
The all-party committee says councils should raise more funds locally, offset by reductions in central taxation.
The MPs also echo a long-standing demand of councils, which is to return the business rate - currently set by government - to local control.
Committee chairman Phyllis Starkey said "radical steps" were needed.
"We are still a long way from an equitable and healthy balance of power between central and local government in this country," she said.
"Central government must take radical steps to tilt the balance of power towards localities, and local government must become more ambitious.
"Much must be done to counter the post-war tendency of governments of all parties to expand their powers at the expense of local government.
"Whilst we fully accept that the government should set strong national strategic goals, it should also pay much greater heed to the benefits of local autonomy."
Dr Starkey said that local authorities should have the flexibility to "vary their priorities to better reflect local aspirations".
She added: "This flexibility should include the ability to raise more of their own money - reducing central taxation if necessary, to ensure that the overall tax burden does not increase."
MPs visited Denmark and Sweden to research their report, which both raise about 70% of their income locally.
The MPs say in both countries, voters can see a much clearer link between local taxes and the quality of services.
Local government minister John Healey said: "We absolutely agree that local authorities are best placed to know what their community needs, which is why the government has already taken unprecedented steps to put more power into the hands of local government.
"We have no plans to change the current structure of council tax or to introduce a local income tax. To do so would create significant restructuring costs and place new burdens on businesses in these tough economic times.
"We will consider the Select Committee's report and respond in due course."