Mr Brown said the "unfair" Air Passenger Duty (APD) adds significantly to the price of flying to and from Scotland and costs millions every year in lost tourism. Following a Yes vote in next year's referendum, the Scottish Government plans to cut APD by 50%, with a view to eventually abolishing the charge.
Halving the fee would mean a family of four flying from Edinburgh to Lapland would pay £26 in tax instead of the current charge of £52, according to the Scottish Government. Mr Brown has received support from management at the three largest airports - Edinburgh, Glasgow and Aberdeen.
Speaking at Edinburgh Airport, he said: "It's clear that the current APD situation puts Scotland at a competitive disadvantage when it comes to attracting visitors and businesses from overseas. It's the most expensive aviation duty in Europe, adding significantly to the cost of flying to and from Scotland."
APD is charged at £13 per passenger each way on a flight up to 2000 miles.