This paper concerns the nonnegative steady-states of the following parabolic system
where is a bounded domain, , , are positive constants and .
This is a Lotka-Volterra prey-predator model with cross-diffusion effects. It is shown tha under certain assumptions (on the parameters) the system admits a branch of positive steady-states, which is or I shaped with respect to a bifurcation parameter. The analysis is based on the bifurcation theory and the Lyapunov-Schmidt procedure.