We present a simulation method to study electroosmotic flow in charged nanopores with dielectric contrast between their interior and the surrounding medium. To perform simulations, we separate the electrostatic energy into the direct Coulomb and the polarization contributions. The polarization part is obtained using periodic Green functions and can be expressed as a sum of fast converging modified Bessel functions. On the other hand, the direct Coulomb part of the electrostatic energy is calculated using fast converging three-dimensional (3D) Ewald summation method, corrected for a pseudo one-dimensional (1D) geometry. The effects of polarization are found to be particularly important for systems with multivalent counterions and narrow nanopores. Depending on the surface charge density, polarization can increase the volumetric flow rate by 200%. For systems with 3:1 electrolyte, we observe that there is a saturation of the volumetric flow rate. In this case, for polarizable pores, the flow rate is 100% higher than for nonpolarizable pores.