<p>In this paper, we study a diffusive predator-prey model with predator-taxis. We examine how predator-taxis influences the stability of the spatially homogeneous steady state and formulate the Turing bifurcation condition. We find that random diffusion alone cannot induce Turing instability. Predator-taxis drives the system from a spatially homogeneous steady state to spatially inhomogeneous patterns. By weakly nonlinear analysis, we obtain the amplitude equation and classify the bifurcation as supercritical or subcritical. Numerical simulations show that predator-taxis induces rich patterns, including stripe patterns, spot patterns, and mixed spot-stripe patterns. Remarkably, as the predator-taxis parameter increases, we observe wave patterns and branching patterns, with pattern amplitudes becoming unstable and growing.</p>