<p>In certain geological conditions, the electrical anisotropy characteristics of media are considered an important influencing factor. Ignoring their impact may lead to incorrect data interpretation. To address this, this paper develops a 3D fast forward algorithm for multi-frequency controlled-source electromagnetic (CSEM) anisotropic media based on model order reduction techniques, to understand the impact of electrical anisotropy characteristics on CSEM data. The paper derives the electric field equations satisfied by CSEM under electrically anisotropic conductivity conditions, discretizes the equation set using unstructured vector finite elements, and combines the shift-and-inverse rational Krylov subspace algorithm to achieve the research of a 3D fast forward algorithm for multi-frequency CSEM in arbitrary electrically anisotropic media. A two-dimensional electrically anisotropic geoelectric model is designed for algorithm testing, and the test results are compared with publicly available algorithms to verify the correctness of the developed program in this paper. To further analyze the algorithm’s efficiency and the impact of electrical anisotropy characteristics on CSEM data, a three-dimensional electrically anisotropic media model is constructed for numerical testing. The test results show that the developed algorithm in this paper can achieve fast forward modeling of multi-frequency CSEM, with an acceleration ratio of more than 10 times, and it is not affected by the number of frequency points. Additionally, the CSEM response of electrically anisotropic media shows significant changes compared to isotropic media, and the single-branch apparent resistivity curves and contour maps can effectively identify the anisotropic principal axis direction.</p>