He's concerned it'll undermine English airports.
The boss of British Airways' owner IAG, said that the move did mark "a major step towards the complete abolition of this stealth tax that hinders economic growth, tourism and jobs".
"However, the piecemeal reduction of APD will only serve to undermine airports in the north of England as passengers will rush across the border to get cheaper flights," Walsh warned. "This will create a domino effect across the whole country which is not sustainable."
To solve this, Walsh wants action taken further. "By abolishing this futile tax, UK GDP would gain 1.7 per cent and create 61,000 new jobs over the longer term," he said.
The Scottish government has confirmed plans to halve Air Passenger Duty by the end of the current Scottish parliament in 2021. Holyrood will take control of the air fare tax from April 2018.
In its 2015 manifesto, the SNP pledged a reduction of 50 per cent, as well as plans to abolish APD in the long run, in an effort to boost more direct flights to and from Scotland.
At the moment every economy class passenger over 15 pays £13 for a short-haul flight or £73 for a long-haul one starting in the UK. The long-haul rate is set to increase by £2 by next April and APD levels are doubled for premium economy, business and first class.
Since March, APD charges have been removed entirely for children under the age of 16,
The Scottish government had said APD continued to act as "a barrier" to Scotland's ability to secure new direct international services.