The Confederation of British Industry says the government should make careers in science, technology, engineering and maths (STEM) more attractive.
It recommends cuts in tuition fees for some STEM subject courses and better training for existing workers.
The CBI argues that key economic sectors are facing a "skills crunch", especially for technicians.
The government says it is investing £385m in STEM university facilities and to support teaching.
CBI members employ a third of Britain's private-sector workforce - and a CBI/Pearson survey suggests that 42% of UK firms faced difficulties recruiting individuals with STEM skills and knowledge last year.
'Engineering our Future'
In a report, called Engineering our Future, the CBI argues that key sectors of the UK economy, from manufacturing and creative industries to the green economy, are facing "a skills crunch".
The report says without help to boost STEM qualifications and more routes into careers based on them, especially for women, businesses will continue to struggle in their recruitment, threatening the long-term health of the economy.
Among its recommendations are a reduction of tuition fees on some STEM courses and the development of one-year cross-over courses.
These would enable 18 year olds to switch back to STEM subjects in preparation for a related degree.
The CBI says a "pressing need" for skilled technicians should be addressed through apprenticeships and retraining, and that firms should be helped to retain older workers in STEM areas.
It also wants to see increased participation in STEM subjects by women, with sixth-form colleges and universities setting themselves gender diversity targets.
'All the talents'
Katja Hall, the CBI's chief policy director, believes future growth and jobs "will depend on the UK having a workforce that can exploit new technologies and discoveries".
She said it was "increasingly clear that the really problematic shortages are at skilled technician level".
"We do have to play a long game on skills, creating more apprenticeships, but we also need policies for the short-term, including retraining existing workers with in-demand skills in key sectors.
"The growing skills vacuum is threatening the recovery, as demand from firms is outstripping supply.
"Highly-skilled workers are essential for our growth sectors and it will be those young people with science and maths who will go on to become the engineers and new tech entrepreneurs of tomorrow.
"The government must explore if it is possible to reduce the costs of some of these courses and create a one-year cross-over qualification at 18 for those who turned away from science and maths after GCSEs, but now want to take a related degree."
The Department for Business Innovation and Skills says it is "committed to ensuring that the science and engineering workforce makes use of all the talents available to it.
"That is why we recently announced a £200m investment in teaching facilities at universities science, technology and engineering and an additional £185m over four years to support teaching.
"The government is also funding a range of programmes including STEMNET, the Royal Society and Royal Academy of Engineering diversity programme which are aimed at encouraging at range of people to study science and engineering."