The claim by Thomas Docherty, who represents Dunfermline and West Fife, is the latest in a series of disputes between Unionist and Nationalist politicians on the key referendum issue of defence.
Last month, the Nationalists insisted official figures showed that during the past five years there had been a £1.9 billion underspend on defence contracts in Scotland.
However, Mr Docherty, who sits on the House of Commons Defence Committee, said he had obtained new Ministry of Defence figures, which showed Scots companies received 25.8% of the sub-contract work on the two carriers.
Of the total £1.2bn worth of sub-contracts, Scottish firms had secured £304m, he calculated.
These include: l £105m to SSSL of Rosyth for painting;
l £57m to Ticon Insulation of Glasgow for insulation linings;
l £16m to Score Marine of Peterhead for valves;
l £13m to MacTaggart Scott of Midlothian for aircraft lifts and
l £4m to McGeoch Marine of Inchinnan for door hatches and manholes.
"This is the UK's foremost civil engineering project of the 21st century and approximately a quarter of the spending on sub-contracts is coming to Scottish engineering and manufacturing firms," said Mr Docherty.
"These figures nail the lie from the Nationalists that Scotland does not get its fair share of defence spending," he added.
Angus Robertson, the Nationalist leader at Westminster, responded by saying: "Tellingly, Labour is not taking issue with official MoD statistics which prove a multibillion-pound structural defence underspend in Scotland. During their years in office, there was a 68% increase in that underspend which now totals more than £7.4bn."
He said Scottish taxpayers and the defence sector in Scotland were "repeatedly short-changed by the MoD".