Based on the modified formula of Rapini-Papoular, the equilibrium equation and boundary condition of the director have been obtained and the behaviour of the Freedericksz transition at the threshold point has been studied for weak-anchoring nematic liquid crystal cells under exteal electric and magnetic fields with the methods of analytical derivation and numerical calculation. The results show that, except for the usual second-order transition, the first-order Freedericksz transition can also be induced by a suitable surface anchoring technique for the liquid crystal cell given in the paper. The conditions for the existence of the first-order Freedericksz transition are obtained. They are related to the material elastic coefficient k11, k33 the thickness of the liquid crystal cell, the exteal electric field and the strength of surface anchoring, etc.