The predator-prey model with superdiffusion is investigated in this paper. Here, the existence of Turing-Hopf bifurcation and the resulting dynamics are studied. To understand such a degenerate bifurcation in the anomalously diffusive system, the weakly nonlinear analysis is employed and the amplitude equations at the Turing-Hopf bifurcation point are obtained. Moreover, by analyzing the amplitude equations under suitable conditions, the abundant spatiotemporal dynamics are presented. In addition, to illustrate the theoretical analysis, some numerical simulations are carried out.