To simulate the elastic wave propagations in 3-dimensional (3D) anisotropic media, a 3D anisotropic lattice model is proposed. The derivation of the general relationship between the anisotropic lattice model and the anisotropic continuum model is presented. With this lattice model, the dynamic lattice method (DLM) is able to simulate elastic wave propagation in arbitrary anisotropic media. Numerical tests on different anisotropic models show that the elastic waves simulated by the DLM coincide with those simulated by the finite difference method, indicating that the dynamic lattice method represents a lattice-based choice for the elastic wave simulation in complex anisotropic media. Our research demonstrates the robustness of the anisotropic lattice model in describing anisotropic media, and lays the foundation for lattice-based methods in terms of elastic wave modeling in 3D anisotropic media.