The YouGov survey found the First Minister faces his biggest challenge among women, where 58% said they did not trust him, against 31% who did.
It follows a question posed over the past week to almost 1200 adults which read: "Generally speaking, how much, if at all, do you trust Alex Salmond?"
The survey appears to show wider concerns over Mr Salmond's leadership, with a degree of distrust expressed among younger people too.
Of the 1192 people questioned between January 21 and yesterday, 57% of those aged 18-24 said they do not trust the SNP leader. However, 30% said they felt they could.
Professor John Curtice, professor of politics at Strathclyde University, said the question could be read pejoratively, potentially reducing the level of trust.
But Professor Curtice added: "The bigger issue about this is it is a single question about Alex Salmond. There is a problem with the lack of context. We know people do not trust politicians, even if they are popular.
"What this does tell us is that even if Alex Salmond is relatively popular there will be a body of people out there whose reaction will be negative.
"It is not evidence he is deeply unpopular."
Among older people and the retired, just over half (55%) of people said they do not trust him, compared to 40% who do. Among the middle-aged (40 to 59), exactly half said they did not trust him, compared to 40% who would.
Generally, among the upper middle class, middle class and lower classes (ABC1s), 58% of those who took part said they did not trust him, compared to 35% who said they did.
Mr Salmond's trust ratings rise slightly to 36% generally among the lower middle class, skilled working class and among casual workers and pensioners (53% do not trust him).
Last month a TNS BMRB poll for The Herald supplement, Scotland Decides, of 1004 people put his popularity higher than Scottish Labour's Johann Lamont, the leader of the No campaign Alistair Darling, and Prime Minister David Cameron. It also put Mr Salmond above his deputy Nicola Sturgeon.
A spokesman for Mr Salmond said: "The reality is that the most recent Mori poll shows the First Minister has the highest level for those satisfied with his performance of all the Holyrood leaders.
"The latest TNS poll shows he is liked more than any of the other Holyrood leaders - four times more than Johann Lamont - and a Panelbase poll last September showed Mr Salmond with net ratings of plus 11, compared to -35 for David Cameron, -46 for Ed Miliband, and -53 for Nick Clegg."
The spokesman also pointed to a poll this week that showed the SNP has a 19-point lead over Labour.
He added this showed "huge trust in the First Minister and Scottish Government - and now required a swing of just over 3% to win the referendum.
He added: "After nearly seven years in office, these are all remarkably positive figures."