We present a discussion of the size-, potential-dependence of the confinement energy in the nanostructure, as well the blue shift due to quantum confinement effect. In this case, we solve the Schrödinger equation by employing two simple models with one-dimensional periodic crystal potential. Results show that the confinement energy increases abruptly as the size of nanostructures decreases. Importantly, the confinement energy no longer strictly follows the size-dependent inverse square formula given by Brus. Furthermore, the band gap and blue shift depend on the crystal potential in the nanostructure, and the confinement energy decreases with the increase of the potential. We also find that the surface bond constriction plays an important role of the confinement energy.