In this article, we investigate the dynamics of interactions between predators and prey in two distinct habitats: the refuge and areas outside the refuge. As the predation pressure decreases, the prey emerges from its hiding place. Predators engage with the prey in the unprotected areas and can even kill them. The behavior of the prey is influenced by the number of predators present, causing them to shift to safer regions. This suggests that when the predator population increases, more prey will seek protection within the refuge, while they will choose to remain outside the refuge when there are fewer predators. By considering the impact of predator density on prey velocity, we incorporated both predator and prey speeds, as well as their anti-predator behavior. The prey has the ability to reduce its velocity to evade attacks. We examined the relationship between anti-predator behavior and prey density and found that prey density increases with a higher level of anti-predator behavior, whether it is due to an increase in predator or prey velocities. Furthermore, we presented evidence that, under specific conditions, the coexisting equilibrium will be globally stable. Additionally, we identified the occurrence of a saddle-node bifurcation at the coexisting equilibrium point.