Based on the modified Rapini-Papoular formula for surface anchoring energy, the saturation behaviour of a weak anchoring nematic liquid crystal cell is studied. The mathematical equations of solving director distribution are obtained. A parameter reflecting the characteristic of director distribution is introduced. Expressions for saturation voltage and the parameter reflecting the characteristic of director distribution are obtained for the second order transition. The methods of calculating the two quantities for the first order transition are also given. The influences of surface polarization on the two quantities are discussed in detail. The results show that whether the second or the first order transition, the position of the maximal tilt angle of director will shift towards the substrates with the increase of surface polarization. The influences of surface polarization on saturation voltage for the second and the first order are reverse. The saturation voltage will increase for the second order but decrease for the first order with the increase of surface polarization.