In an interview with the BBC, Marta Andreasen - who was ditched from her post as chief accountant at the European Commission in May - says the Commission's numbers fail even to meet minimum accounting standards.
Officials can change numbers without leaving any kind of electronic trail, offering a standing temptation to fiddle the figures, Ms Andreasen said.
The charges come at an embarrassing time, just as the world is trying to tighten the rules after a spate of accounting irregularities committed by large private corporations.
Ms Andreasen's allegations are repeated in the Financial Times newspaper, which on Thursday published details of what it said were leaked documents from the EU's court of auditors.
The Commission's systems are "out of control" with "obvious risks as regards reliability", the paper quotes the report as saying, and says the commission "has been warned about them but to date has not taken any action".
Closed book
Ms Andreasen told the BBC's Today programme that the systems at the Commission made accurate record-keeping impossible.
"The effect of all this is that the accounts do not present a true and fair view of the situation at the commission," she said.
"The computer system on which the transactions are processed is incoherent, insecure and allows no audit trail."
The lack of security, she warned, "gives big room for fraud" - and makes tracking it almost impossible.
Off the case
Ms Andreasen was moved to a job with few responsibilities on her old 125,000-euro salary in May after refusing to sign off on the Commission's 2001 accounts.
She had been pressured to do so by senior officials, she said, and is now facing disciplinary action initiated by Neil Kinnock, former UK Labour Party leader and now Commission vice-president in charge of administration.
The Commission itself has strongly disavowed her claims.
Mr Kinnock has said the problems were already well-rehearsed and were being dealt with by the time Ms Andreasen began her complaints.
And the Commission said her sideways move was the result of personnel problems.
The FT's report agreed with this up to a point, noting that the problem first came to light in auditors' reports in 1999 and 2000 covering the then-new Sincom 2 system.
But it added that the leaked document from the court of auditors, dated February 2002, said little or nothing had been done since.
"No account has been taken of generally accepted accounting standards, mainly double-entry book-keeping," it warned.