Abstract: In the 2-D inhomogeneous media, the magnetotelluric problem can be taken as one on propagation of electromagnetic wave in the dissipitive open waveguide, and is attacked with the numerical modematching method (NMM).First, the problem domain is sectioned into several subdomains, in each of which the resistivity changes only along the horizontal direction.Then the governing equation is separated into two differential equations.One equation relates to z variable and has analytical solution, while the other relating to y variable is computed with numerical method.The electromagnetic fields between different subdomains are related through the continuous conditions of the electromagnetic field.While the dimension of the problem is reduced to one, the demand for the computer resources decreases apparently and the speed increases substantially.In order to further improve the efficiency of the algorithm, the Hermite basis functions and the inhomogeneous elements are used in Ex problem, and the modified Hermite basis functions are used in Hx problem.Comparison with the finite element method (FEM) shows that NMM is at least ten times faster than FEM.