A 3D DC finite element method forward program is developed in this paper for anisotropic geoelectric media. Both total and secondary field approaches have been implemented. In this paper, we focused on the structured grid scheme. The modeling shows that the symmetry of the structure grid determines the symmetry of the response potential around the point source for an anisotropic half-space. Through numerical modeling with three kinds of coarse meshes by the total field approach and secondary field approach separately, a higher accuracy can be achieved via the secondary field approach. And the relative error between the numerical solution and the analytical solution is less than 2%. Modeling results contrasting with previous scholars also verify the correctness of the algorithm. Then, the numerical results of 3D models with anisotropic properties were presented and compared to models with isotropic properties. These results clearly illustrated the strong effect of anisotropy and the problems in interpretation if anisotropy was not properly addressed. This work will establish the foundation for our future effort of building a 3D inversion program with arbitrary anisotropy.