This article concerns the nonlinear Dirac-Poisson system −i 3 X k=1 α k ∂ k u + (V (x) + a)βu + ωu − φu = Fu(x, u), −∆φ = 4π|u| 2 , in R 3 , where V (x) is a potential function and F (x, u) is an asymptotically quadratic nonlinearity modeling various types of interaction. Since the effects of the nonlocal term, we use some special techniques to deal with the non-local term. Moreover, the existence of infinitely many stationary solutions is obtained for system with periodicity assumption via variational methods.