In this paper, we study an eigenvalue problem for Schrödinger-Poisson system with indefinite nonlinearity and potential well as follows: -Δu+μV(x)u+K(x)Φu = λf(x)u+g(x)|u|^p-2u in R³, -ΔΦ=K(x)u^2 in R³, where 4≤p<6, the parameters μ, λ>0, V∈ C(R³) is a potential well, and the functions f ∈ L^3/2(R³) and g ∈ L^∞(R³) are allowed to be sign-changing. It is well known that such a system with the potential being positive constant has two positive solutions when lim_|x|→∞g(x)=g_∞<0, K=0 in the set {x ∈ R³ : g(x)=0} and λ>λ₁(f) with near λ₁(f), where λ₁(f) is the first eigenvalue of -Δ+ id in H¹(R³) (see e.g. Huang et al., J. Differential Equations 255, 2463 (2013)). The main purpose is to obtain the existence and multiplicity of positive solutions without the above assumptions for g and K. The results are obtained via variational method and steep potential. Furthermore, we also consider the concentration of solutions as μ→∞.