A survey of more than 1,000 members of the Institute of Directors (IoD) found that a third were struggling to fill vacancies because of a shortage of suitably qualified applicants.
One in four firms had so-called "skills shortage vacancies", said the IoD, while half of directors believed some of their employees were not skilled enough.
Miles Templeman, director general of the IoD, said: "It is disturbing that at a time of economic weakness, the growth of the private sector is being held back by skills shortages.
"Businesses want to invest in training and are doing so on a large scale already, but they would invest even more if the government took some radical steps to deliver a better overall business environment.
"Excessive employment regulation and an uncompetitive tax system effectively eat up resources that businesses could use to fund training.
"The government needs to put more emphasis on sorting out these problems if it wants to tackle skills shortages. The biggest barrier to greater employer investment in training is a lack of resource, not a lack of law."
A Department for Business spokesman said: "The government recognises skills are essential if we are to return to sustainable growth. To achieve this we want to give learners the funding, support and information they need to make the right choices for their future.
"We are putting apprenticeships at the heart of the system, boosting the numbers of places available to adults across the country, as well as ensuring those who have left school without basic skills in literacy and numeracy have access to free training."