Glasgow Airport handled more than 693,000 passengers in May, up 4.3% on the same month last year.
International traffic rose 6.9% while domestic passenger numbers increased by 1.6%.
The airport said growth was driven primarily by Thomson, Lufthansa and KLM adding capacity on European routes, while Jet2's fifth Glasgow-based aircraft also began operating during the month.
Virgin Atlantic and US Airways added capacity on their North American routes, while demand for flights to London continues to drive domestic growth, the airport said.
Amanda McMillan, managing director of Glasgow Airport, said: "May always gives us a taste of what to expect during our busiest months, with the summer timetable well under way and a real buzz in the terminal.
"With less than 50 days to go until the opening ceremony of the Commonwealth Games in Glasgow, our focus now is to ensure that our multimillion-pound investment programme is completed in time. The check-in hall is looking fantastic and the improvements we are making to the international arrivals area are well under way.
"We are also working with a range of partners to ensure Glasgow Airport is ready to play its part in delivering a successful and memorable event for the city."
Aberdeen Airport also saw a rise in passenger numbers in May, with 327,469 people passing through - up 6.7% on the same month during the previous year.
Of that growth there was a 7.4% increase in fixed wing passengers and a 3.2% rise in the helicopter sector.
Airport managing director Carol Benzie said: "The first few months of this year have been strong for the airport and to be able to announce that trend continuing is very encouraging.
"We have seen growth in both the domestic and international markets; in fact international growth has performed particularly well.
"Over the past few weeks we have seen the launch of new flights for summer 2015 and have been able to add a route to Faro to our destination portfolio.
"Whilst our further route development work continues, this means that one of the top three requested destinations is now going to be served from Aberdeen. We are pleased that our airline partners are in a position to offer our customers extra choice which I am sure will be well received."
Edinburgh Airport announced its passenger figures yesterday.
A total of 937,093 passengers travelled through the airport last month, a 3.5% increase on May 2013.