The BMG Research survey carried out for The Herald showed Nicola Sturgeon’s party on 43 per cent in the constituency vote, ahead of Labour on 17 per cent, the Scottish Conservatives on 13 per cent and the Liberal Democrats with 5 per cent.
In the second regional list vote, the SNP was on 37 per cent, Labour on 16 per cent, the Conservatives on 13 per cent, the Greens 6 per cent, Lib Dems 5 per cent and Ukip 3 per cent.
However, nearly one in five voters said they were still undecided ahead of the May 5 election.
It comes after a Panelbase poll for the Sunday Times put the Scottish Conservatives and Labour neck and neck in the race for second.
The survey of 1,021 people suggested Ruth Davidson’s party could overtake Kezia Dugdale’s.
Support for Labour in the constituency vote was at 19 per cent, slightly ahead of the Tories on 18 per cent. In the regional list vote, the Conservatives edge ahead of Labour, on 19 per cent and 18 per cent respectively.
Backing for the SNP was at 51 per cent and 47 per cent.
In the BMG Research poll of 1,013 Scots, those surveyed were also asked about Scottish Labour’s proposal for a 1p rise in income tax to be spent on protecting education and other services.
Support for the policy was at 51 per cent compared with 21 per cent opposed, but that backing dropped eight percentage points when voters were told it was a Labour proposal. The biggest falls were among SNP and Conservative backers, with a a rise among Labour supporters.
The poll also found 55 per cent of Scots want to stay in the EU compared with 35 per cent who want to leave.
Asked whether a second referendum on independence should be triggered if Scotland was taken out of the EU against the will of Scottish voters, 43 per cent were in favour and 45 per cent against.
A Scottish Labour spokesman told The Herald: “This poll confirms strong support for Kezia Dugdale’s plan for fairer taxes, including a 50p top rate of tax for the richest 1 per cent, to stop the cuts and invest in education.
“Faced with the choice between using the powers of the Scottish Parliament to invest in our economy or carrying on with the SNP’s cuts, Labour will use the powers.”
A spokesman for the SNP said: “This is another very encouraging poll for the SNP, and we will step up our campaign right across Scotland this week as we launch our manifesto.”