The study, by the Royal Academy of Engineering, says 100,000 Stem graduates are needed a year just to maintain the status quo.
It argues the UK is already slipping down the international innovation league tables.
The UK has dropped to eighth globally in the number of US patents registered.
The report estimates 830,000 graduate-level Stem experts and 450,000 technicians will be needed by 2020.
In the UK some 23,000 engineers are graduating every year. But India is producing eight times as many, and China 20 times as many.
The report warns overall that the current pool of science, technology and engineering experts are already "stretched thin" and ageing rapidly. The median age of chartered engineers rises by 10 years for every 14 that pass.
UK firms are already having to recruit experts from abroad.
The report adds that the requirement for 100,000 Stem graduates per year between 2012 and 2020 will not be met by newly graduating students alone, and calls for Stem experts to be trained through other routes.
"With only circa 90,000 Stem graduates each year (including international students who presently cannot obtain visas to work in the UK after graduation) and knowing from earlier analysis of Hesa [Higher Education Statistics Agency] data that a proportion of Stem graduates choose non science occupations (26% of engineering graduates for example) there are clearly too few UK Stem graduates to meet the need," it says.
Prof Matthew Harrison, director of engineering and education at the Royal Academy of Engineering, said the shortage of Stem graduates was getting worse.
"In the last 10 years the general wage premium for graduates has been dropping, but over the same period the graduate premium for engineering has been going up.
"Engineering firms are crying out for engineers. They can't get the people they need. Although they have been very very vocal about the subject it has not translated into public policy yet."
A Department for Business, Innovation and Skills spokesman said it was working closely with industry and continue to look at various ways to support engineering at all levels, including engagement in schools, apprenticeships and postgraduate training.
"We have recently committed £3m to create up to 500 additional aeronautical engineers at masters level over the next three years, co-funded with industry," he said.
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