The NHS trust which runs Peterborough and Stamford hospitals has said 300 jobs could go as part of £38m of cuts.
The hospital trust, which employs 3,500 people, said it would also be saving money by making the hospital more efficient.
A spokesman for the trust said the cuts were needed due to the increasing costs, such as increasing drug prices facing hospitals across the country.
The authority's 2011/2012 budget was set by a meeting of the trust's board.
Nigel Hards, chairman of the Peterborough and Stamford Hospitals NHS Foundation Trust, said: "We presented our income and expenditure budgets for 2011/2012 which shows a financial gap of £38m in the coming year.
"This is a serious financial situation, in line with many other acute hospitals, and we are working to address this challenge while absolutely maintaining the safety and quality of care for our patients.
"We have already put measures in place to reduce spending across all areas and are building a robust savings and efficiency plan.
"However, to help us deliver these savings, we need to remove around 300 posts from across the trust.
"We will seek to minimise the number of redundancies by taking steps including reducing our temporary workforce (agency staff) and by not filling non-essential vacant posts."
He added: "Most of our savings will be made in the next two years, but it is likely to take three years to achieve our plans.
"While this is an important challenge for the trust, we will work with all our stakeholders including patients, staff and partner organisations to ensure our absolute priority remains the safety and care of our patients."
The trust spent £207m in 2009/2010, £225m in 2010/2011 and the trust set a budget of £206m in 2011/2012.