Considering the exciton effect, the polarizability and second polarizability spectra of semiconducting single-wall carbon nanotubes (S-SWCNTs) have been calculated by PPP (Pariser, Parr, and Pople) approximation and the single-excitation configuration interaction (single-CI) method and sum-over-state method. We have studied the nonlinear optical (NLO) properties of the S-SWCNTs with different lengths and diameters. The highest and first peak positions, bandgap, and the spectra shape of the polarizability and second hyperpolarizability change as N (the number of atoms) increases. Also, the peak values of γzzzz are very bigger than that for γxxxx. Our results indicate that the nonlinear optical properties of fullerenes are similar to S-SWCNTs.