The frequency-dependent moment (FDM) method proposed by Iwata [Chem. Phys. Lett. 102, 544 (1983)] has been applied to the calculation of the second- and third-order frequency-dependent polarizabilities. It is demonstrated that the FDM ab initio calculations on the HF molecule give the same numerical results as the sum-over-state (SOS) calculations. It is important that the FDM requires only the ground-state eigensolution of the CI matrix while the SOS requires all the eigensolutions. Calculations were also made on H2O and CH4. The FDM method becomes very effective when the CI matrix is so large that its direct diagonalization becomes formidable.