<p>In this paper, we investigate the traveling wave solutions of a nonlocal dispersal predator–prey system with stage structure in the prey species. It is well known that the traveling wave solutions can describe the invasion process of an alien predator into the habitat of indigenous prey with stage structure. By constructing an invariant cone in a bounded domain with initial functions being defined on, employing the method of upper and lower solution and Schauder’s fixed-point theorem, we first prove the existence of nontrivial super-critical traveling wave solutions connecting the predator-free equilibrium at negative infinity. Then, the persistence of traveling wave solutions is given, and the asymptotic behavior of traveling wave solutions at positive infinity is derived by constructing a suitable Lyapunov functional. Next, by the limiting argument and detailed analysis technique, we obtain the existence of critical traveling wave solutions. These results indicate the occurrence of invasion-coexistence phenomenon. Finally, we prove that the system has no nontrivial traveling wave solution by using a contradictory approach with the properties of the corresponding characteristic equation to the system.</p>