It condemned "the misogynist, hateful comments" made by Trump, the Republican presidential nominee, about women and minorities, BBC reported on Thursday.
It follows the release of a 2005 video last week in which Trump makes remarks about groping women.
He has apologised for remarks, which he described as as "locker-room talk".
He has also denied touching women inappropriately.
The motion was filed by Greens party MP Jeremy Buckingham to the Upper House of the NSW parliament. It said: "This house... agrees with those who have described Mr Trump as a 'revolting slug'."
"It's clear that all reasonable and decent people find Donald Trump's behaviour obnoxious and that the world is hoping American voters reject his politics of hate," Buckingham said in a statement.
As there was no objection, the motion was recorded as having been agreed to by all of the lawmakers.
It was allowed only after the president of the legislative council determined that "revolting slug" did not amount to unparliamentary language. Parliamentary procedure prevents MPs from using "extremely distasteful" words.
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