Transportation and Works Minister Nick McGrath says the cost is expected to be about $56 million, up from the original $40-million price tag in 2009 to renovate the building in St. John's.
The work includes the replacement of windows and brick as well as repairs to the tower.
It is the first major overhaul of the building since it opened in 1960.
McGrath says costs rose after crews discovered limestone around the windows had deteriorated, requiring the replacement of entire window casings.
Liberal critic Tom Osborne says some new windows are already leaking and he expects costs will only rise once window blinds are installed.
But McGrath says any leaks will be covered under warranty, and not all windows will require blinds.
The work is expected to be completed next year.