The existence of positive steady-state solutions of a two species predator-prey model，in which the predator is partially coupled with alternative prey is investigated. By means of lower and upper solutions, a priori estimate of the non-negative steady-state solutions of the system is given. Taking the intrinsic growth rate of the prey population r as a bifurcation parameter, the concrete form of solutions bifurcated from the positive constant solution is given by local bifurcation theory and the local bifurcation solutions can also be extended to infinite by using global bifurcation theory.

predator-prey model; alternative prey; Holling-type Ⅱ; global bifurcation