An extra 260,000 passengers used the airport compared with the same month in 2014, mainly due to an increase in long-haul flights and larger aircraft.
In June, Gatwick said it had the busiest year in its history, claiming it proved its case for a second runway.
The Airports Commission has since backed a new Heathrow runway instead.
Gatwick said demand for long-haul flights to New York, Los Angeles, Cape Verde, Trinidad and Costa Rica had contributed to the increased passenger numbers.
It said it had now experienced two-and-a-half years of consecutive month-on-month growth.
Gatwick's chief executive Stewart Wingate said the July figures showed his airport remained the best location for the new runway.
"These results put us 10 years ahead of the forecasts used by the Airports Commission to predict future air traffic movements," he said.
"Our growth in the last 12 months is actually more than the commission concluded could be added at Gatwick in the first year of a new runway.
"This is further proof of the flaws in the Airports Commission analysis and shows its conclusions are fast unravelling."
A spokesman for the commission said: "All forecasts in the Airports Commission final report were subject to extensive analysis and we are confident that they are fit for purpose."

The rare plants around Dinas Bran, a medieval castle and iron age hillfort above Llangollen and the Dee Valley, have been awarded national recognition.
Natural Resources Wales says important species of birds and butterflies "rely on the grassland and other habitats".
It is also home to upright chickweed, shepherd's cress and greater broomrap.
"The grasslands found here are scarce in lowland Britain," said Richard May, conservation officer for NRW.
"And Dinas Bran has the second largest area in Wales of one type of acid grassland."
The remains of Dinas Bran castle and hillfort date back to the occupation of the princes of Powys Fadog in the mid 13th century and they have been protected since 1957.
"Dinas Bran is hugely popular with walkers, attracting thousands of people a year to visit the iron age hillfort and medieval castle set in a spectacular landscape," added Mr May.
"By working in partnership with landowners, we look forward to helping to manage the site's special features so that we and future generations can continue to enjoy Dinas Bran's rich natural and historical heritage."
Gatwick had its busiest July with 4.3 million passengers - a 6.4% increase on last year - the West Sussex airport has said.
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A "scarce" grassland around the ancient ruins of a Denbighshire castle has been protected as a site of special scientific interest.