Propagating constants of rectangular waveguide loaded with dissipative slab obey complex transcendental equation, of which the property of multiroot and the dependence of modes on those roots often make people puzzled, especially for dissipative magnetic materials in an asymmetrically filling situation. An effective new algorithm combining Genetic Algorithm (GA) with Parameter Tracking Scheme (PTS) and Dynamic Searching Area (DSA) technique is developed. By using the algorithm, the propagating constants of waveguide symmetrically or asymmetrically loaded with dissipative magnetic slab are solved successfully and tightly linked to certain designated modes. The results also reveal some interesting phenomena, such as for some high-order modes and certain thickness of loaded slab, the negative phase velocity may occur.