In this paper, we study the existence and multiplicity of p-Laplacian elliptic problems –Δpu=a(x)us+λ(x)ut on bounded domains Ω⊂RN(N⩾3) with indefinite sublinear nonlinearities under Dirichiet boundary conditions. That is,we get the first solution by using the sub-super solution,and then the second solution is obtained by applying the relaxed Mountain Pass Theorem.