Announcing the move on Twitter, SNP councillor Christopher McEleny said the role had given him "invaluable" experience in politics.
He pushed for the "Plan B" resolution at the party's conference that would bypass the need for a second referendum on independence if a majority in Scotland voted for pro-independence parties at the next Holyrood election.
Nicola Sturgeon and other senior party figures rejected the move - which was also backed by at least one MP - saying that a referendum was the only feasible and legally watertight way to guarantee independence.
Mr McEleny received a hostile reception from some delegates at the party's recent annual conference in Aberdeen.
In a statement posted on social media, he said: "I have been lucky to be at the sharp end of politics for the past seven years and the experience I have gained is invaluable.
"It is for that reason that I believe the party will be stronger as a whole if others are afforded the opportunity to gain the experience I have benefited from as the council group leader, therefore I shall be stepping down as SNP leader in Inverclyde."
He said he would continue to serve as a councillor.