In a letter to the company's worldwide workforce, Les Alberthal complains of poor morale, growing client dissatisfaction and falling share prices.
The letter, a copy of which has been passed to The Independent, was sent out a week before Labour came to power, yet only two weeks ago the company was awarded a pounds 53m contract to upgrade air traffic control systems over the North Atlantic.
Mr Alberthal told the EDS workforce that much good work was being done but he added: "...we still see a number of things that worry us. Employee turnover is increasing and morale is not where we want it to be. We have not done as good a job with our clients as we should have.
"Our shareholders have told us they are unhappy with our performance, and our first-quarter earnings ... underscored questions about how fast EDS can continue to grow."
Staffing levels would, he said, have to be trimmed by about 9,000 from about 100,000 employees worldwide.
The results showed a fall in earnings of 11 per cent worldwide. Shares fell from $63 last year to a low of $32.50, although the company continues to be successful in the UK and has contracts with the Inland Revenue, the DSS, the Child Support Agency, the Ministry of Defence, the Paymaster General and many more.
Mark Fox, a spokesman for the company, said Mr Alberthal's letter was intended to show that staffing costs could not grow faster than revenue but it did not mean the company was overstretched.