A high-order mixed-edge rectangular element method is proposed for analysis of lossy dielectric guiding structures.The emphasis is laid on the investigation of the space construction of the high-mixed-order edge rectangular element and the explicit form of the shape function is given. The method provides a direct solution for propagetion constants wrthout the spurious solutions. The computationsof the propagation constants for the eigen modes in the rectanguar waveguide and slab loaded waveguide show that the accuracy of the high-order mixed-edge element approach is about one order higher than that of the lowest-order one. The calculations of the dispersion for the dominant mode in a lossy dielectric loaded waveguide verify the accuracy and efficiency of the present method.