<p>In this study, a predator–prey model incorporating prey’s fear effect and anti-predation behavior has been developed. The functional response takes the square root of the prey population and adds the predator’s loss term. We prove the existence of the system’s equilibrium point and derive the conditions for its local stability, as well as discuss how diffusion affects the system’s stability. Bifurcation analysis of the parameters reveals that the fear effect leads to a decrease in the predator population in the coexistence equilibrium. In addition, we apply the finite difference method and the finite element method to simulate the diffusion model in rectangles and irregular customized regions, respectively. The results demonstrate that the system can eventually reach a uniform stable state after experiencing oscillations and fluctuations at certain parameters and initial values.</p>