Though he claimed for travel of 5,100km in July, trips recorded in his official diary only account for 884km, documents released under freedom of information legislation show.
Mr Quinn’s department said an itemised record of his car trips for July has not been kept.
“The electronic diary maintained by the minister’s office does not reflect all official use of the minister’s car,” said a spokesman.
“An itemised list of car journeys is not available.
“The new travel arrangements introduced by ministers have resulted in annualised savings of 70% in respect of Minister Quinn’s travel.”
Ministers are banned from claiming mileage for journeys that were taken for personal or party political reasons, but do not have to submit details of all journeys in order to receive claims.
Mr Quinn claimed the €1,451 for mileage in July.
Mr Quinn was in America for six days in July, and a further seven days are listed as private or blank in his official diary.
Only one of his official engagements in July was outside Dublin — a visit to the MacGill summer school in Co Donegal.
Ministers sign a form at the end of each month to state how many kilometres they have travelled on official duties.
For the four months between May and August last year, Mr Quinn made 16,800km of mileage claims, worth €6,751.65.
Mr Quinn’s department has been at the centre of a bitter row over cutbacks, with special needs assistants and schools in socially deprived areas amongst those targeted for spending reductions.