Detection of electrical anisotropy of geologic formations is an important problem that has attracted the attention of geophysicists for nearly 70 years. The newly developed multi-component device such as triaxial induction tool can detect formation anisotropy and provide more information in reservoir evaluation. In this report, we present a 3-D finite-difference (FD) method to simulate multicomponent induction log responses in arbitrarily anisotropic media. The generalized anisotropy of the medium is described by a symmetric 3×3 conductivity tensor. The finite-difference method uses a staggered grid to approximate the vector equation for the scattered electric field. The resulting large linear sparse system is solved iteratively by the generalized minimal residual (GMRES) algorithm in frequency domain. An incomplete LU preconditioner is developed to improve the convergence behavior of the system equation, thus accelerate the solution. In addition, the optimization grids specially developed for the finite-difference grids is applied to minimize the error at the receiver locations and approximate the boundary conditions at infinite, which reduces the grid sizes and thus the computation time required for the log simulations. The results of the present method will be verified by comparing with those of the integral equation method using the same meshes. The Comparisons of the results with those in the published papers will be conducted to demonstrate the accuracy of the algorithm. Our further development includes speeding up the code, parallelization of the software, and providing a way of easy use of the code.