In this paper, we consider a coupled k-Hessian system Sk(D2u)−λ1um+vp+f(u,v)=0inΩ,Sk(D2v)−λ2vn+uq+g(u,v)=0inΩ,where Ω⊂RN is a ball, Sk(D2u) stands for k-Hessian operator. By applying the linearization technology and the implicit function theorem, we state and certify the non-degeneracy and uniqueness of the positive radial solutions to a coupled k-Hessian system.