This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder's fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant $c^{*}$ such that when $c>c^{*}$, the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with $c=c^{*}$ is also established by a limiting argument and a delicate analysis of the boundary conditions. Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed $c

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