Smoke can be seen across the city as flames erupted behind Wills Memorial Building.
It is believed the fire started in the new Bristol University maths building – the Fry building.
It is undergoing refurbishment and is due to open in spring.
SWNS
Will Marsh, head of media at the University, said: “The fire is in the Fry Building, our maths building which was undergoing a refurbishment and was due to open later this year, in spring time.
“We believe no one was inside at the time, but it is still very sad news.”
The fire is in the old part of the university, in Park Street in the city centre.
SWNS
TWITTER
Surrounding roads have been closed and nearby buildings are understood to have been evacuated.
People took to Twitter after seeing the fire.
Bobby Mason said: "Looks like a big fire in Bristol somewhere near Park Street. Hope everyone is OK #BristolFire".
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While Tim Collins wrote: "Bristol Uni fire looks pretty insane at the moment. I really do hope everyone is okay up there."
Avon Fire and Rescue FBU wrote on Twitter: "Thoughts with crews dealing with incident in Bristol right now. Hopefully not as bad as it seems. Plz give crews room to work & be patient if delayed."
The Fry Building formerly housed the University's School of Biological Sciences until 2014.
Huge fire at Bristol University. pic.twitter.com/mW5kyRbxlD
— Graeme Poole (@DrGraemePoole) January 6, 2018
It is on a triangular site between Woodland Road and University Road with the Wills Memorial Tower to the south.
It was part of a £33million investment by The University of Bristol to transform the Grade II listed building.
The building would have become the new home for the university's School of Mathematics and included lecture theatres, teaching rooms, quiet study areas and social spaces.
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New additions to the historic building were to include an atrium linking to a new 140-seat lecture theatre with a roof garden above.
The fire is at the heart of the university campus and flames could be seen from across the city.
Helicopters were being used by emergency services to guide jets of water being shot at the inferno.