But while the Trust welcomed members' views, it said the resolution could not be implemented in its current form as it was not possible to write clauses into existing tenant contracts.
At the charity's Annual General Meeting last Saturday, members voted 50,412 in favour of the resolution, with 12,575 votes against and 22,459 abstentions.
The strongly-worded proposal from members demanded that the Trust ban all its farm tenants from growing any GM crops on Trust land, citing concerns such as the impact on Britain's wildlife and ecosystem.
It urged the Trust to ensure that the final word on the planting of GM crops on its land will be "a conscious decision of the Trust and not forced by the current short-term consideration of GM technology."
The proposal sparked a lively debate at the AGM, reflecting the high emotions and conflicting views on the issue of GM crops among National Trust members.
David Riddle, director of land use at The National Trust, said: "We feel that the vote actually reflects our current position on GM crops. There are so many uncertainties and unanswered questions surrounding the issue of GM and we don't want to jump into anything that we don't fully understand.
"We will wait until the final outcome of the Government's reports into GM so that we can make an informed decision."
At the meeting, the Trust warned that although its income was up 17 per cent to £76m in 2002/3, it still needed further revenue growth to secure the future of its properties and conservation programmes.