A new high order edge element approach is discussed. This method not only elimiflates the spurious solutions but also possesses the characteristics of simplicity and high efficiency. The emphasis is laid on the investigation of the space construction of the second-order edge-element approach and the related formulations are given.The computations of the eigenvalues of the dominant and the higher-order modes in the slab loaded waveguide show that the accuracy of the second-order edge-element approach is about one order higher than that of the first-order edge-element approach.The calculations of the dispersion curves for the dominant mode in the block dielectric loaded rectangular waveguide and in the microstrip line with anisotropic substrate verify the accuracy and the extensive suitability of the present method.