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."
Gatwick had its busiest July with 4.3 million passengers - a 6.4% increase on last year - the West Sussex airport has said.