In this paper, we study initial-boundary value problem of a predator-prey model with taxis strategies and a nonlinear growth rate for the predator. We establish that, for any spatial dimension $(N\ge 1)$, the model admits positive classical solutions that are globally existent and uniformly bounded. Our results demonstrate that the nonlinear growth rate can effectively restrain the aggregation of predators. Furthermore, by constructing a suitable energy functional and combining it with the previously established uniform boundedness result, we analyze the global asymptotic stability of the coexistence steady state.