Three-Dimensional (3-D) ICs are able to obtain significant performance benefits over two-dimensional (2-D) ICs based on the electrical and mechanical properties resulting from the new geometrical arrangement. The arrangement of 3-D ICs also offers opportunities for new circuit architecture based on the geometric capacity. The emerging 3-D VLSI integration and process technologies allow the new design opportunities in 3-D Network-on-Chip (NoC). The 3-D NoC can reduce significant amount of wire length for local and global interconnects. In this paper, we have proposed an efficient 3-D Asymmetric Torus routing algorithm for NoC. The 3-D torus has constant node degree, recursive structure, simple communication algorithms, and good scalability. A Quadrant-XYZ dimension order routing algorithm is proposed to build 3-D Asymmetric Torus NoC router. The algorithm partitions the geometrical space into quadrants and selects the nearest wrap-around edge to connect the destination node. Thus, the presented algorithm guarantees minimal paths to each destination based on routing regulations. The complexity of the algorithm is O (n). The proposed routing algorithm has been compared with the traditional XYZ algorithm and the comparison results show that the Quadrant-XYZ router has shorter path length. This paper presents a Register Transfer Logic (RTL) simulation model of Quadrant-XYZ dimension order routing algorithm for 3-D asymmetric torus NoC written in Verilog. The model represents the functional behavior of the routing chip down to the flit (byte) level. The 3-D asymmetric torus NoC has achieved a maximum operating frequency 750 MHz on Xilinx Vertex-6 programmable device.