The asymptotic stability of monotone decreasing kink profile solitary-wave solution for generalized river-bed model equation was mainly studied. Firstly, by using the theory of planar dynamical system, the existence of kink profile solitary-wave solution of this equation was proved. Secondly, three properties of the monotone decreasing kink profile solitary-wave solution were proved, especially the first-order and second-order derivative estimation formulas of this traveling wave solution were given. Finally, by using anti-derivative strategy, with the help of priori estimate and Young inequality, it was proved that the monotone decreasing kink profile solitary-wave solution of model equation was asymptotically stable.