A total of 746,000 people passed through Glasgow Airport during August, a rise of 6% compared with the same month last year.
The airport had its busiest summer since 2008 with almost 2.4 million passengers over June, July and August.
Edinburgh Airport, officially Scotland's busiest, had more than a million passengers in August, the second month in a row in which the milestone was reached.
Meanwhile the number of people using Aberdeen International Airport grew by 3.5% over the month, to 312,200.
Glasgow Airport's growth was attributed to airlines adding extra capacity as well as high-profile events such as the World Pipe Band Championships being held in the city.
Managing director Amanda McMillan said: "We enjoyed an extremely busy summer with more than 125,000 additional passengers using the airport during June, July and August compared to the same period last year.
"Not only was it our busiest summer in five years, it was one of our best in terms of operational performance. Despite the significant increase in numbers and a host of large-scale events, 99.4% of our passengers passed through security in less than 10 minutes during the summer months."
Edinburgh recorded 1,082,938 people passing through its doors in July. The figure for August was 1,035,997, a rise of 10.6% on the previous year.
Chief executive Gordon Dewar said: "What a summer we've had. We were over the moon to see one million passengers in July but to report the same record-breaking milestone in August is fantastic.
"The ever-increasing popularity of the Edinburgh summer festivals, coupled with the good weather, has obviously continued to attract visitors from all over the world to Scotland's capital.
"It's great to think that we've welcomed enough passengers over the last two months to fill all 67,800 seats of Murrayfield stadium 30 times, roughly the population of Houston, Texas."
Helicopter traffic at Aberdeen fell 11.5% on the previous year, a result of the Super Puma helicopter crash off Shetland last month in which four oil workers died.
Carol Benzie, the airport's commercial director, said: "As one of the worlds' busiest heliports, the sad events of the 23rd August impacted on the whole airport community and our thoughts go out to the families involved.
"We are working closely with all of the on-site helicopter operators to understand the challenges that they are going to be facing in coming weeks and months.
"The beginning of September saw the city enjoy a very successful Offshore Europe (conference) and the airport operation coped well with the influx of visitors to the region. Whilst the total numbers are still to be released, initial estimates suggest it may be another record breaker."