Considering the significant impact of anisotropy on forward and inversion results, this paper presents a research study on tensor controlled-source audio magnetotellurics (CSAMT) forward modeling in axis anisotropic media. In this study, the tensor resistivity of axis anisotropic medium is introduced according to the control equation of electric field with sources. The total electric field is decomposed into primary and secondary fields, with the primary field obtained using Key’s algorithm and the secondary field calculated using the finite difference method. This approach enables three-dimensional (3D) modeling of tensor CSAMT in axis anisotropic media. The correctness of the algorithm is verified by comparing it with the results obtained using a two-dimensional (2D) finite element algorithm. Several sets of axis anisotropic 3D models are designed, and the response characteristics of anisotropic target bodies to plane waves and non-plane waves are summarized. The findings indicate that the Cagniard resistivity and tipper are sensitive to changes in the X and Y directions of the anomaly, but not sensitive to changes in resistivity in the Z direction. Additionally, in the near region, non-plane wave CSAMT signals may cause distortion in the Cagniard resistivity. The results highlight that tensor CSAMT has the capability to detect changes in resistivity in two-axis directions (X and Y), providing greater exploration advantages compared to scalar CSAMT. This study provides a foundation for the forward modeling and inversion of tensor CSAMT in arbitrary anisotropic media.