The poll puts Labour in front, but with the Green Party quickly gaining ground and the Liberal Democrats slipping into a distant third. The junior Coalition partner’s vote is down 28 percentage points since the last election.
The Green swing in Bristol comes after the party won a number of council seats in the area since the last General election.
Darren Hall, Green Party Candidate for Bristol West and the Green Party’s Home Affairs spokesperson, said:
“Anyone who has spent any time on the streets of Bristol West in the last few months will know we can and will win here on May 7th.
“People in Bristol are increasingly recognising that a Green MP would give them a strong independent voice in Parliament.
“People in Bristol West understand that we need the real change for the common good offered only by Greens. A strong Green grouping in Westminster on May 8 can make a genuine difference.
“I'll never back a Tory government, and I'll work to ensure that any Labour Government has backbone on issues like austerity, Trident and climate change."
A spokesperson for the Green Party said: "Despite all of their bluster it is clear that the Liberal Democrats are finished in Bristol West. It's a two-horse race between Labour and the Greens and the momentum is certainly with the Greens.”
The Green Party of England and Wales is polling at its highest ever levels ahead of a General Election.
On Tuesday. the Green Party Leader, Natalie Bennett, will be in Bristol launching the Green Party's campaign bus tour. She's expected to give a speech on the Green Party's opposition to benefits cuts.