The existence of positive solutions of the steady-state system of a predator-prey model with strong Allee effects is discussed.By using local bifurcation theory and regarding the growth rate d of the predator as bifurcation parameter, the local bifurcation branch from the semi-trivial solution branch is investigated, which can be extended to global bifurcation branch by global bifurcation theory. The sufficient conditions for the existence of positive steady-state solutions are gained.It is shown that the model has coexistence solutions whenever the growth rate of the predator d∈λ1-mu*2a+u*2, λ1-mu*1a+u*1, the parameter b∈0,12(which reflects the intensity of strong Allee effect), and the inherent growth rate of the prey α>α*.

strong Allee effect; positive solution; global bifurcation