The UK Border Agency (UKBA) - recently branded "not fit for purpose" - paid £3.5m in performance-related bonuses to staff in one year, the BBC has learned.
Passengers recently faced prolonged queues to enter the UK at London's Heathrow airport, while the UKBA's computer ID system failed on 3 May.
The figures from a Freedom of Information request show the highest bonuses in the past year were £10,000.
The Home Office said bonuses were only given when staff achieved high results.
But Labour MP Keith Vaz, chairman of the home affairs select committee, described himself as "shocked" at the outlay.
"The agency has been plagued by failures, including the relaxation of border controls, an inability to clear the asylum backlog, and the reluctance to tackle bogus colleges through unannounced inspections," he said.
"Rewarding this failure with payments of up to £10,000 is unacceptable.
"The committee recommended in January 2011 that no bonuses should be paid to senior staff."
The BBC understands at least two individuals received £10,000 bonuses.
Mr Vaz said in light of the disclosure he would be raising the issue of bonuses with both the immigration minister and the chief executive of the UKBA when they come before his committee on Tuesday.
The figures are for the most recent financial year available, 2010-2011.
That was before the UK Border Agency was divided from the UK Border Force, now responsible for front line immigration staffing.
The Freedom of Information request also shows between 2008 and 2011, for which figures are available, more than £11.1m of taxpayer's money was paid to staff in bonuses.
A spokeswoman for the Immigration Services Union said that bonuses for front line staff are capped at £250, suggesting that the "vast majority" of these bonuses went to senior management.
She went on: "The taxpayer should have the right to say if they would prefer a functioning and properly resourced secure border - or these significant increases the salary packages of senior civil servants involved in this debacle.
'Failing on basics'
"The sum budgeted for bonuses [in one year] would pay for over 100 fully trained border officers."
The UKBA has had a troubled couple of years.
In April it was accused by the home affairs committee of providing "inconsistent" information about immigration and asylum cases dating back to 2006.
A backlog of 450,000 cases is expected to take four years to clear.
Keith Vaz MP said then it was "failing on basics" and "not fit for purpose".
In 2011 another report found that 40% of immigration cases in the UKBA's backlog were given permanent right to stay in the UK - a rate so high it "amounted to an amnesty", something the organisation denied.
The UKBA was also accused of "dumping" a number of immigration cases equivalent to the population of Cambridge in a special archive, effectively giving up on them.
In November 2010, there were 18,000 cases in this archive - but the committee said over the next 10 months that rose to 124,000.
There was controversy over revelations that hundreds of thousands of people were let into the country without complete checks when border controls were relaxed, again in 2011.
It led to the suspension of UKBA chief Brodie Clark, who later resigned.
And in February of that year an independent report found the UKBA was failing to take action against hundreds of migrant workers who had no right to stay in Britain.
Meanwhile, in December 2010 there was criticism after customs officers at Heathrow Airport were told not to stop suspected drug smugglers in the run-up to Christmas because of a lack of resources.
A spokesman for the Home Office, the umbrella organisation for the UKBA, pointed out that the median bonus was just over £500.
He said: "Bonus payments are kept under constant review and are only awarded when staff have performed to strict criteria.
"No permanent member of staff received a bonus of more than £10,000 in 2010/11."
With regard to the series of controversies to have dogged the agency in recent times, Coalition ministers have regularly blamed the situation they inherited on coming to power.
The UKBA was set up in 2008, two years after then Labour Home Secretary John Reid said the Home Office's immigration directorate was "not fit for purpose".
His predecessor, Charles Clarke, was sacked after it emerged 1,013 foreign nationals had been released from prison without being considered for deportation.
By 2012, 397 of them had been removed or deported, while 57 have not been located.