The main purpose of this paper is to investigate positive solutions of the following system of integral equations with weight Riesz potential on Ω: $$\left\{\begin{array}{ll} u(x)=\int\limits_{\Omega}{|x|^{-\alpha}|x-y|^{-\mu}|y|^{-\beta}}{u^a(y)v^b(y)}dy,\\ v(x)=\int\limits_{\Omega}{|x|^{-\gamma}|x-y|^{-\nu}|y|^{-\kappa}}{u^c(y)v^d(y)}dy,\\ \end{array} \right.$$ where a, b, c, d, α, β, γ, κ, μ, ν are constants. With the method of moving planes, we establish the symmetry of both the solution and the bounded C 1 domain Ω if u and v are constants on ∂Ω. Moreover, we also give a symmetry result for systems of integral equations with weight Riesz potential on exterior domains.