  This paper is concerned with positive solutions of boundary value problems
\begin{equation*} \left\{\begin{array}{ll} {\rm div}\left(d(v)\nabla
u-u\chi(v)\nabla v\right)+\lambda u-u^2 +\gamma u F(v)=0, & x \in
\Omega,\\[1mm] D \Delta v+\mu v-v^2-u F(v)=0, & x \in \Omega,\\[1mm] u=v=0, & x
\in \partial \Omega. \end{array}\right. \end{equation*} This is the stationary
problem associated with the predator-prey system with prey-taxis, and $u$
(resp. $v$) denotes the population density of predator (resp. prey). In
particular, the presence of $\chi(v)$ represents the tendency of predators to
move toward the increasing preys gradient direction. Regarding $\lambda$ as a
bifurcation parameter, we make a detailed description for the global
bifurcation structure of the set of positive solutions. So that ranges of
parameters are found for which the system admits positive solutions.
