Delegates at the party's annual conference in Perth approved a motion calling for the UK Government to hand over power of APD to the Scottish Parliament to allow Holyrood to scrap it.
The conference heard Scottish airports lose two million passengers a year because of the charges.
Paisley MSP George Adam, whose neighbouring constit-uency includes Glasgow Airport, said Glasgow needs to attract more direct routes but APD was preventing airlines from locating at the airport.
He said: "The airport is a catalyst for investment in the area, but APD costs two million passengers a year. That cannot continue.
"By nature of our geography we need to be connected to Europe and the world, but there has been a decrease in short-haul flights of 60% since 2007. We need to be able to support the companies in this industry and this is a perfect example of why Scotland should be independent."
At a separate event at the conference, Transport Minister Keith Brown said if the UK government gave Scotland control of the tax it would be scrapped.
He said: "There is unanimity across the aviation industry that APD is a bad thing for our airports and the economy.
"If we are given the powers we will eliminate it and the Scottish Government will take that cost. The Calman Commission recommended it but nothing has happened.
"The ability to take our own decisions with APD would be a quick game changer."
Mr Brown said there was much work going on to attract new airlines and destinations to Scotland's airports but APD was a barrier.
He said a service from Mexico could have come to a UK airport but there were two reasons why the airline chose Paris instead.
One he said was APD and the other was visa problems.
He said 300 people a week were going to Paris rather than coming to the UK and possibly to Scotland.
That is one example of how APD is working against us."
The motion proposed by Colin Keir MSP and Angus Brendan Macneill MP said the reduction of APD would boost the UK economy by 5% over three years, be worth £5billion a year and create around 60,000 jobs.
South of Scotland MSP Chic Brodie also backed the call stating other countries in Europe had abandoned their flight taxes after they were found to cost more in lost revenue than they raised in tax.