A simplified model is used to describe the nonlinear optical behaviors of absorption and refractive index change of semiconductors. Based on engineering the semiconductor band, the optical absorption spectrum and the dispersion of the refractive index change are calculated by means of the density-matrix theory. The dependence of absorption coefficient and refractive index change on the optical intensity is shown. The numerical results show that near the bandgap the change in refractive index is remarkable. A trade-off of optical absorption and index change should be taken for the practical nonlinear optical devices.