1 Preview Construction Inc. stated that the price range in building a covered deck costs around $3,000 to $8,000. 2  This estimation is good for a wood deck and includes the materials and the labor. The specific prices vary according to the quality. 2  A 200 square foot deck, for example, could cost $1,471 – $1,679 for the best quality deck and around $1,068 to $1,506 for a lower quality one.