Attention is focused on a new method to reduce the numerical dispersion of the 3-D Alternating-Direction Implicit Finite-Difference Time-Domain(ADI-FDTD) method through artificial anisotropy. As the wave propagation can be speeded up by introducing proper anisotropy parameters into the 3-D ADI-FDTD method, the numerical dispersion can be reduced and the accuracy can be improved significantly. First, the numerical formulations of the 3-D ADI-FDTD method are modified. Secondly, the new numerical dispersion relation is derived. And consequently the relative permittivity tensor of artificial anisotropy can be obtained. In order to demonstrate the accuracy and efficiency of this new method, a hollow waveguide and a waveguide with discontinuous structure are simulated as examples. In addition the reduction of numerical dispersion is investigated as a function of the relative permittivity tensor of artificial anisotropy. Furthermore, the numerical results and the computational requirements of the proposed method are compared with those of the conventional 3-D ADI-FDTD method. It is found that this new method is accurate and efficient.