Accenture won the NIRS2 contract in 1995 despite bidding £100m less than its rivals in a deal that was subject to a previous NAO investigation.
Sandy Gordon, NAO's audit manager, said: "We will be looking at the decision to award the contract extension to Accenture without competition.
"The report will not cover the operation or implementation of the original system. But the previous problems with NIRS2 were a major factor in the decision to publish a report into the contract extension award."
NIRS2 has been plagued by problems since the award of the original contract.
Accenture - then called Andersen Consulting - paid £3.9m in compensation for delays in 1997 and 1998 that led to delays in government payments to UK pension companies worth £1.5bn.
At the height of the problems, NIRS2 produced a backlog of pensions and benefits miscalculations which left 120,000 pensioners underpaid by £41m, and led to pensions minister Jeff Rooker branding the IT system as "rubbish".
The NAO will examine why additional development work was contracted, what options were available to the Inland Revenue for carrying out this additional work, and how such options were evaluated in the absence of open competition.
The report will also investigate what steps the Inland Revenue has taken to ensure problems with the original contract are not repeated during the course of the additional work.
"This review is one of the NAO's regular routine audits of aspects of the department's activities," a Revenue spokesman said. "The main audit work has already been completed. As usual, we have provided the assistance and information the NAO require."
A spokesman for Accenture added: "All IT systems have teething problems but in terms of functionality the system is operating fairly well. Recent reports from the NAO have recognised that we have made significant progress with NIRS2."
The NAO report will be published in December.