This paper study the following a kind of predator-prey system-a system of weakly coupled elliptic partial differential equations with homogeneous Dirichlet conditions -d1△u=au-a_1u2-a_1f1(u)v x∈Ω -d2△v=bv-b_1v~2+b_2f2(u)v x∈Ω u=v=0 x∈ where d1

d2

a1

a2

b1

b2 are positive constants

a and b are real parameters

Ω is a bounded domain in Rn with smooth boundary

and fi(i=1

2) fullfil some conditions. The existence and uniqueness of positive solutions of the system(0.1)is proved by using sub and supersolution technique

bifurcation theory and decoupling method.