In all of the classical force fields, electrostatic interaction is simply treated and explicit electronic polarizability is neglected. The condensed-phase polarization, relative to the gas-phase charge distributions, is commonly accounted for in an average way by increasing the atomic charges, which remain fixed throughout simulations. Based on the lipid polarizable force field DMPC and following the same framework as Atomic Multipole Optimized Energetics for BiomoleculAr (AMOEBA) simulation, the present effort expands the force field to new anionic lipid models, in which the new lipids contain DMPG and POPS. The parameters are compatible with the AMOEBA force field, which includes water, ions, proteins, etc. The charge distribution of each atom is represented by the permanent atomic monopole, dipole and quadrupole moments, which are derived from the ab initio gas phase calculations. Many-body polarization including the inter- and intramolecular polarization is modeled in a consistent manner with distributed atomic polarizabilities. Molecular dynamics simulations of the two aqueous DMPG and POPS membrane bilayer systems, consisting of 72 lipids with water molecules, were then carried out to validate the force field parameters. Membrane width, area per lipid, volume per lipid, deuterium order parameters, electron density profile, electrostatic potential difference between the center of the bilayer and water are all calculated, and compared with limited experimental data.