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The paper deal with the existence of positive solution for the following (p,q)-Laplacian nonlinear system align* { arrayll -Δ_pu=a(x)(α_1f(v)+β_1h(u)), & x∈Ω, -Δ_qv=b(x)(α_2g(u)+β_2k(v)),& x∈Ω, u=v=0,& x∈∂Ω, array . align* where Δ_p denotes the p-Laplacian operator defined by Δ_pz=div(|∇_z|^p-2∇z), p>1, α_1, α_2, β_1, β_2 are positive parameters and Ω is a bounded domain in R^N(N > 1) with smooth boundary ∂Ω. Here a(x) and b(x) are C^1 sign-changing functions that maybe negative near the boundary and f, g, h, k are C^1 nondecreasing functions such that f, g, h, k: [0,∞)→[0,∞); f (s), g(s), h(s), k(s) > 0; s > 0 and lim_n→∞f(Mg(x)^1q-1 x^p-1 =0 for every M > 0. We discuss the existence of positive solution when f, g, h, k, a(x) and b(x) satisfy certain additional conditions. We use the method of sub-super solutions to establish our results. , number=2, journal=Journal of Partial Differential Equations, year=2013, month=June, pages=99–106