The rate currently goes up by 2% above inflation each year but the All-Party Parliamentary Group on Smoking and Health wants that increased to 5%.
It says an extra £100m per year would be generated to spend on anti-smoking projects and the rate of decline in smoking would be doubled.
Tobacco manufacturers described the proposal as "counterproductive".
The MPs recommend that spending on anti-smoking schemes should be increased from £200m a year to £300m, which would be funded by the increase in tax.
In their report, being submitted to the Treasury's Comprehensive Spending Review, they also said cutting the number of smokers would reduce demand on the NHS.
Group chair Bob Blackman, Conservative MP for Harrow East, said: "The APPG on Smoking and Health calls on the chancellor to increase tobacco taxes and invest in tobacco control in the forthcoming Spending Review.
"Smokers don't just die early, they suffer many years of disease and disability before they do, putting pressure not just on the NHS, but additional disability and social care costs and reduced income tax.
"Every pound invested over the next five years could deliver £11 to the public purse."
The Tobacco Manufacturers' Association said tobacco tax had increased by more than 40% over the past five years - and that the UK had Europe's most expensive tobacco.
"Every time taxation is increased on tobacco it loses the Treasury millions that could have been spent on public services," said its director general Giles Roca.
Forest, an organisation that describes itself as the friend of the smoker, said higher taxes would lead to more people buying tobacco abroad or on the black market.
Tax on tobacco should be raised to persuade smokers to quit, a parliamentary group says.