A catalytic reaction model, the Ziff-Gulari-Barshad model, is studied on fractal lattices, and the influence of the order of ramification of the lattice on the dynamic behavior of the model is investigated. According to the Monte Carlo simulation results, the order of ramification of the lattice is not crucial to the existence of the continuous transition. This is different from the equilibrium phase transitions in discrete-symmetry spin models such as the Ising model!. Our results indicate that the criterion of the existence of the reactive phase may be complicated.