Using both numerical simulations and an analytical theory we study the influence of the surface order-electricity polarization and flexoelectric polarization on the bistable state of a non-xymmetric weak anchoring nematic liquid crystal cell at saturation point.The equilibrium equation and boundary condition of the director have been obtained when surface order-electricity polarization and flexoelectric polarization coexistence. By adopting a new state parameter, the physical effects caused by the two polarizations have been discussed from the energy point of view. The results show that the bistable state can be induced under certain condition and by changing the anchoring energy at saturation point. The condition for the bistable state existence is deduced and it accord well with the numerical results.