Hornsey library, a grade II-listed building in Crouch End, will get an extra £2.3 million to enable critical maintenance work to take place.
The 55-year-old building on Haringey Park is in a poor state of repair and suffers from a leaking roof and windows, crumbling wall panels and a faulty boiler.
In 2015, it was granted £1 million as part of a modernisation programme designed to improve its interior.
The council now says extra work is needed to ensure it is fit for purpose and meets building regulations.
Work is due to start on site in January 2019 and will take around seven to eight months to complete.