The NHS in England paid out over £1.1bn in 2014/15 to lawyers and to patients who suffered harm, new figures show.
This coming year it will be £1.4bn, said the NHS Litigation Authority.
The body said it would work with other parts of the NHS to reduce costs and improve safety and learning.
Chief executive officer Helen Vernon said: ''Negligence claims place increasing pressure on the health service, frontline staff, our members and ultimately patients."
"It is one area of the NHS where no-one would argue against a reduction.''
The NHS in England has seen an increase in costs associated with clinical negligence claims in recent years, although the figure last year was slightly higher at £1.192bn.
The authority said in its annual report that several factors were involved, including an increase in the number of patients being treated on the NHS.
It also said there was an increase in the number of reported incidents, although this could be due in part to a positive reporting culture.
The Medical Defence Union, which provides medical indemnity to doctors, said the money paid out by the NHS to compensate patients could have funded over eight million MRI scans.
Dr Michael Devlin, head of professional standards and liaison, said: "The cost of care is the main reason for the staggering negligence bill.
"The money paid is no reflection on clinical standards, which remain high, but it reflects the unsustainable cost of private sector health and social care packages.
"We have to stop money haemorrhaging out of the NHS in compensation awards. Today's figures only accentuate the need for a complete rethink of personal injury law."
Last month, the government said it intended to put strict limits on the "excessive fees" some lawyers claim in medical negligence cases against the NHS in England.
Officials have called for a defined limit on legal costs in cases where the claims are below £100,000, saying that some lawyers submit bills that charge more than patients receive in compensation.
Solicitors have warned the move could deny patients access to justice.