Edinburgh Airport saw a rise of 11.5% on January 2013, with 586,184 passengers passing through the terminal last month.
At Aberdeen Airport there was a rise of almost 10% while Glasgow experienced a 6% increase.
Edinburgh Airport said its international traffic was up 14.3% on January 2013, with a total of 264,682 passengers passing through last month.
It handled 321,502 domestic passengers, up 9.4% on the previous year.
Gordon Dewar, the airport's chief executive, said: "We've enjoyed a strong start to 2014 with our domestic carriers seeing a steady increase in passenger numbers in January.
"The introduction of Virgin Atlantic's Little Red service to Heathrow has seen an extra 25,000 passengers travel through Edinburgh Airport compared to the same time last year.
"We've also performed well internationally, with Lufthansa doubling their daily service to Frankfurt during the winter season and the new European services from easyJet seeing their passenger numbers increase 12% from January 2013.
"We've hit the ground running for 2014 and are gearing up for what promises to be a very busy few months, with thousands of French rugby fans arriving in March and over a dozen new routes launching in the spring. We're confident we can continue to provide our passengers with a great airport experience."
Almost 251,400 people passed through Aberdeen Airport last month, a rise of 9.8% on the same month last year.
Both helicopter and fixed-wing passenger numbers grew, by 17.8% and 8.5% respectively.
Airport managing director Carol Benzie said: "2014 is now well under way, and to be reporting a strong set of results gives us confidence in the future.
"This year will not be without its challenges, not least working hard to ensure that our terminal redevelopment plans can continue at pace with minimal disruption to passengers.
"These passenger numbers also strengthen the case we make in our ongoing discussion with airlines around new routes as we continue to try to improve our leisure travel offering. We are all hopeful that this positive trend in passenger growth can continue."
More than 436,000 passengers travelled through Glasgow Airport last month, up 6% on the same period last year.
The airport said that domestic traffic grew by 4% benefiting from strong demand for Glasgow's London routes while international traffic grew by 9%, with airlines such as Lufthansa Regional, KLM, Jet2.com and Emirates all reporting an increase in demand.
Amanda McMillan, managing director of Glasgow Airport, said: "January is traditionally a quiet month so it is very encouraging to have made such a positive start to 2014. Our growth was largely driven by demand for international travel, particularly long-haul traffic which was up 10%, but it was very pleasing to see our domestic routes perform so well.
"2014 will present a fantastic opportunity to grow the inbound tourism potential of the city and we are committed to playing our part. Our preparations for the Commonwealth Games are now at an advanced stage and people will start to notice real changes within the terminal building in the coming weeks and months.
"Other large-scale events such as the MTV Music Awards and the Ryder Cup will showcase Glasgow to the world and the recent confirmation that Hampden Park will host the London leg of the IAAF Diamond League was yet further good news for the city."