The poll by Survation, commissioned by the Sunday Post, found that once undecided voters were stripped out Scottish Labour were on 25 per cent, up eight points from a similar poll on April 23.
The SNP are on 40 per cent (down three points) while the Tories are on 27 per cent (down one point) and the Lib Dems are on 6 per cent (down three points).
Analysis by the Scotland Votes seat predictor suggested that the SNP would lose ten seats, the Sunday Post reported.
This would leave the SNP with 46 seats (down from 56), while the Tories would secure seven (up from one), Labour three (up from one) and the Lib Dems three (up from one).
The poll showed that 11 per cent of voters are undecided, down from 18 per cent in April.
Survation carried out the survey of 1024 Scots between May 31 and June 2.
On the issue of tactical voting respondents were asked if they would consider voting for a party or candidate that is not their first choice in order to stop a party or candidate they do not like from winning.
A total of 44 per cent said Yes, 34 per cent said No and 22 per cent were not sure.
The poll also looked at the Scottish independence question.
It found that 54 per cent of respondents would vote No in another independence referendum while 46 per cent would back Yes.
However, 40 per cent said that they were more likely to support independence if another Tory government were elected.
Meanwhile, 14 per cent said this would make them less likely to back independence while 38.5 per cent said it would make no difference and the rest didn’t know.