We present a new, extended, predator-prey model for which we discuss the role of predators mobility and hunting effectiveness on the dynamics of the system. We show, via Monte Carlo simulations, that the maximum of predators' population density is a rather complex function of both – mobility and effectiveness of hunting. For a low mobility, larger effectiveness suits the predators better. When the mobility is large, the predators population is bigger if the predators are rather bad hunters. We have not observed temporal oscillations in the densities of both species.