3D-NoC has emerged to provide fast and power efficient connection between the layers of 2D-NoCs using Through-Silicon-Vias (TSV). Thermal stress, warpage, impurities and misalignment during the manufacturing process make these expensive TSVs vulnerable to faults. Chips with faulty TSVs should be either discarded or utilized by providing a proper fault-tolerant method. In this paper, we target designing a reconfigurable fault-tolerant routing algorithm capable of tolerating fabrication-time or run-time TSV failures. The proposed algorithm ensures a fault-free communication between any two nodes in the presence of TSV failures. Experimental results show that the proposed fault-tolerant routing algorithm provides 100% reliability as long as there is one healthy TSV in the eastmost or westmost column. The reliability of the counterpart algorithm, the Elevator-first routing algorithm, drops to 75% and 45% in presence of one and two faulty TSVs, respectively.