Almost 50,000 people have joined the party following the No vote on independence on September 18, taking the total membership to more than 75,000.
The party overtook the Liberal Democrats to be the third largest party in the UK last week.
SNP business convener Derek Mackay said the surge in new members shows no signs of stopping.
He said: “The strong position of the SNP - standing at 49% in the polls - contrasts starkly with the Westminster parties.
“We’ve now well overtaken the Lib Dems at UK level - whose membership is 44,000 - and the Tories and Labour are tearing each other apart as their vow to the people of Scotland gets caught up in the infighting between Westminster factions.
“With this extraordinary growth in membership, it is clear that it is the SNP that the people of Scotland trust to hold the Westminster establishment to account on their vow of substantial more powers for Scotland.
“This new democratic movement in Scotland simply won’t accept the same old politics as usual from the No parties - Westminster now simply must deliver the real powers we need to make Scotland a fairer, more prosperous country for everyone who lives here. Failure to do so would be completely unacceptable.”
The independence-supporting Scottish Greens have also experienced a surge in membership, with more than 6,000 now signed up to the party.