The Commons Public Accounts Committee said HMRC was set to achieve less than half the projected savings from reducing fraud and error in the payment of tax credits.
The 2010 spending review set HMRC a target of saving £8 billion by 2015, but the committee said that it now estimated it would miss its goal by £5 billion.
In 2010/11 alone, it lost £2.3 billion due to error and fraud - £850 million more than expected - with one-in-five awards of tax credits thought to have resulted in the claimants being overpaid. The following year it wrote off £1.7 billion in tax credit debts as uncollectable.
Although the committee said that HMRC had massively increased the numbers of checks it carried on individuals from 123,000 to almost 2 million, it had only resulted in a doubling of the money saved.
"HMRC needs a better understanding of its performance as it hugely overestimated its progress in tackling error and fraud," the committee said. "HMRC needs to make more effective use of available data to prevent and detect errors and fraud."
An HMRC spokesman said: "In the last four years we have boosted our targeted checks on tax credit claims 10 times over, more than doubling the money protected, saving £390 million in three key risk areas alone.
"Work with the private sector has improved the data we use to make sure claimants' information is accurate and fraudulent claims identified. We are also getting tougher with claimants about the proof they need to support their claims, for example on childcare costs and on school leavers. From 2014 the new Real Time Information system will provide accurate and up-to-date information for tax credit claims, significantly reducing fraud and error. We will continue to improve the service and quality of information we provide, while clamping down on the minority who seek to abuse the rules."
A Treasury source added: "Gordon Brown created this system. We are clearing up his mess. Labour cut the number of people in HMRC tackling fraud and error - the coalition is increasing them."