The survey shows that 37% of people will vote yes in the referendum - up five percentage points - while 44% will vote no. A further 19% of voters do not know how they will vote.
The poll was conducted by ICM between January 21 and 24, surveying 1000 people over 16.
Chief executive of Yes Scotland Blair Jenkins said: "The poll represents a significant swing to Yes."
Better Together leader Alistair Darling said the referendum will be "far closer than people think".