A magnetotelluric finite‐element modelling algorithm is developed, which is capable of handling three‐dimensional conductive and magnetic anisotropic anomalies. Different from earlier three‐dimensional magnetotelluric anisotropic modelling methods, the algorithm we presented has taken the magnetic anisotropy into consideration. The variational equations are produced by the Galerkin method and the governing equations are solved using a hexahedral vector edge finite‐element method. The accuracy of this algorithm is firstly validated by comparing its solutions with the results of finite‐difference method for a three‐dimensional conductive arbitrary anisotropic model, and then validated by comparing with analytical solutions for a one‐dimensional magnetic model. The responses of four kinds of models under different conditions are studied, and some conclusions are obtained. It shows that for materials with a high magnetic permeability, its influence on magnetotelluric responses cannot be ignored in some circumstances. Especially, if the magnetic susceptibility is exceptionally high, it may really distort the apparent resistivities of lower resistive anomalies. These conclusions are also beneficial for magnetotelluric survey.