The currently empty commercial building is being expanded and modernised with a new glazed atrium to be created and the front façade given a facelift.
The 58,000 sq ft waterfront building on Floating Harbour is owned by the Standard Life Heritage With Profits Fund.
The work is expected to be finished by spring 2015.
Derek Quinn, Executive Director at Midas Construction, said: "Narrow Quay House is a fantastic project involving a major transformation of a very prominent commercial building in the centre of Bristol.
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"The logistics of carrying out the internal renovations are challenging and involve a lot of careful planning, with a complex steel frame installation needing to come through the front entrance and be erected within the building to create the extra floor space, for example.
"The existing façade will be removed from the outside of the building and a dramatic new design created, with a double height entrance to Princes Street.
"The development is of a very high quality, with our client, Standard Life Investments, and ourselves working closely with AWW Architects to create an extremely high-end office development to benefit Bristol city centre."
(CD/JP)
