In this paper, the Cauchy problem for the bipolar Navier-Stokes-Poisson system is studied. We obtain the global existence and the Hs decay rate of classical solutions for this problem. Our approach is mainly based on the analysis of the Green's function of the linearized system and some elaborate energy estimates. It should be mentioned that with the help of long wave-short wave decomposition, the decay rate of the higher order derivatives of the solutions is obtained. Furthermore, based on the Hs decay rate of the solutions, we also give the Lp estimate of the solution.