The party say it will give Scotland's ailing economy a much-needed boost by tapping into the lucrative markets of China, the US west coast and central America.
Talks have already taken place with the SNP Government which also wants to axe APD through the new powers coming to Holyrood under the Smith Commission. A bill is due to be published setting out ministers' APD plans in the next few weeks.
The Tories had opposed any move to cut APD in this year's Holyrood election but say the slump in Scotland's economy since then means action is now needed. The party is also supporting an immediate APD freeze on short-haul flights to the UK and Europe, in order to ensure passengers can also enjoy cheaper fares to destinations nearer to home.
Tory finance spokesman Murdo Fraser said: “APD is one of the new powers of the Scottish Parliament coming our way thanks to our proposals to strengthen devolution.
“As we prepare for Brexit, it is more important than ever to use these powers to go global, so we can create new jobs, deliver more opportunities, and build a stronger economy.
“Abolishing APD for long-haul flights has the potential to do just that for Scotland. Airlines will be incentivised to put on new direct long-haul flights from Scotland.
“That means instead of having to go via London or Amsterdam, families and businesses would be able to get on a plane in Edinburgh or Glasgow and fly direct to China or the USA, or other global destinations."
Air passenger duty is charged on all passenger flights from UK airports, with the rate of tax varying according to where the passenger is going, and the class of travel, starting at about £13 for short-haul flights to Europe.
It brings in about £3bn a year for the UK government. The Scottish government wants to use new powers being devolved to Holyrood to reduce APD from Scottish airports by 50% from April 2018 before eventually abolishing the tax altogether.