Summary: In this paper we study the existence and stability of nonconstant positive steady states to a reaction-advection-diffusion system with Rosenzweig-MacArthur kinetics. This system can be used to model the spatial-temporal distributions of predator and prey species. We investigate the effect of prey-taxis on the formation of nonconstant positive steady states in 1D. Stability and instability of these nonconstant steady states are also obtained. We also perform some numerical studies to support the theoretical findings. It is also shown that the Rosenzweig-MacArthur prey-taxis model admits very rich and complicated spatial-temporal dynamics.