Abstract: The application of MECHL finite element to Maxwell's equation on anisotropic meshes is mainly investigated. By proving a new lemma together with the known high accuracy estimates of this element, the superclose and superconvergence results of the backward Euler and Crank-Nicolson-Galerkin fully discrete schemes are given. At the same time, a numerical example is provided to verify the theoretical analysis. The results further show that the regularity condition on the subdivision in traditional finite element analysis is not necessary, and thus the defects of the previous literature are overcomed.