In this work, the optical absorption coefficients and the refractive index changes for the infinite and finite semi-parabolic quantum well are calculated. Numerical calculations are performed for typical GaAs / Al x Ga 1-x As semi-parabolic quantum well. The energy eigenvalues and eigenfunctions of these systems are calculated numerically. Optical properties are obtained using the compact density matrix approach. Results show that the energy eigenvalues and the matrix elements of the infinite and finite cases are different. The calculations reveal that the resonant peaks of the optical properties of the finite case occur at lower values of the incident photon energy with respect to the infinite case. Results indicate that the maximum value of the refractive index changes for the finite case are greater than that of the infinite case. Our calculations also show that in contrast to the infinite case, the resonant peak value of the total absorption coefficient in the case of the finite well is a non-monotonic function of the semi-parabolic confinement frequency.