This paper is devoted to the numerical approximation of the ionospheric Dynamo model in a non‐uniform magnetic field. The numerical difficulty to solve this model comes from the anisotropy of the elliptic equation describing the electric field. This anisotropy causes the associated linear system of elliptic equation to be ill‐conditioned, when solved with standard methods. We present an asymptotic preserving method in this paper to solve this anisotropic equation, such that its linear system is independent of the anisotropy.