A predator-prey reaction-diffusion model with a fear factor and hunting cooperative is studied to explore the effects of two factors on the behavior of the predator-prey system dynamics. The local asymptotic stability of the positive equilibrium point is analyzed by the characteristic equation of the positive equilibrium point. The Hopf bifurcation point $\alpha^*$ is obtained by taking the hunting cooperation coefficient $\alpha$ as the bifurcation parameter without considering the fear factor. When the cooperation coefficient is greater than $\alpha^*$, the fear factor is used as the bifurcation parameter to obtain the Hopf bifurcation point $e^*$, the spatially homogeneous and non-homogeneous periodic solutions are generated near the Hopf bifurcation point. In addition, the conditions of Turing instability caused by diffusion are discussed. The results show that the system has a spatially inhomogeneous steady state when the ratio of predator and prey diffusivity is small. These conclusions can provide theoretical basis for how to maintain ecological balance. Finally, the conclusions are verified by numerical simulation.