Aberdeen Airport said 343,405 people used the hub in June, an increase of 9 per cent on the same period last year.
At Glasgow, passenger numbers were up 2.5 per cent owing to a growth in demand for European services.
The airport said it is now gearing up for the influx of athletes and visitors for the Commonwealth Games which opens on July 23.
Aberdeen managing director Carol Benzie said the further growth is “even exceeding our expectations”.
She said: “Of course, rapid growth brings with it challenges from an operational perspective, but we are working hard to make sure we can keep the airport running smoothly in the face of construction projects and the influx of customers.
“We ask anyone using the airport to ensure that they are prepared for security over the summer months. With new routes coming on stream and an increase in holiday traffic we are at the beginning of a busy time at Aberdeen International Airport.”
There was growth of 9.4 per cent in fixed wing flight passengers at the airport and 6.8 per cent in helicopter passengers.
More than 793,000 people travelled through Glasgow, contributing to a 1.7 per cent rise in domestic traffic and a 3.1 per cent increase in international passengers.
The airport said it was a particularly strong month for Irish carrier Aer Lingus, which recorded its busiest month at Glasgow Airport since 2002 after carrying more than 18,000 passengers.
Commercial director Francois Bourienne said: “June represented the start of the busy summer season and we were pleased to continue our trend of passenger growth. Airlines responded to demand by adding extra capacity on popular routes and we also welcomed the launch of new services such as easyJet’s direct flights to Split, Croatia.
“Our focus is now firmly on helping to deliver a successful Commonwealth Games. There are only 12 days to go until the opening ceremony and there is a real sense of excitement and anticipation building at the airport.”