Abstract: A theoretical model was proposed under mean-field approximation,specially including abnormal diffusion on fractal surface,to describe behavior of nonlinear dynamics in a typical dimer-monomer model: CO+O₂.The Oscillatory behavior and kinetic phase transition were studied intensively.（1）As decreasing of fractal dimension,the oscillatory regimes shift to lower CO pressure,shrink,and vanish finally.A kind of fractal-induced oscillation,resulted from limited diffusion,found.（2）At higher temperature,fractal structure controls not only nonlinear dynamics behaviors but also kinetic phase transition from high-covered state to low-covered state of CO.Lower dimension structure may drive the transition from the first order to second one.But this situation does not appear at low temperature,where fractal control only moves the critical point,but it is not enough to change the transition order.