Controlled-source audio-frequency magnetotellurics (CSAMT) is an important geophysical technique. Numerous studies have shown that the electrical anisotropy in the Earth cannot be ignored because it would probably lead to misinterpretations of electromagnetic data. It is necessary and meaningful to study CSAMT responses in three-dimensional (3D) electrical anisotropic media; therefore, we have developed an edge-based finite element method for 3D CSAMT forward modelling in generalised anisotropic media. The total electric field in this approach is decomposed into a primary electric field and a secondary electric field, and the Galerkin weighted residuals method is adopted to obtain the variational equation. The accuracy of this algorithm was initially validated by comparing solutions with those obtained in previous work on a 3D arbitrary anisotropic model. We then studied the responses of an oblique source as well as equatorial and axial configurations and the tensor source for anomalies with different Euler's angles. Several meaningful conclusions can be derived from this work and a synthetic model is developed; the results also confirm the validity of previous conclusions. This study shows that a tensor source is necessary for a CSAMT survey in 3D anisotropic media, and the anisotropic parameters of anomalies have complex and significant influences on CSAMT responses.