The electronic spectra and optical properties of one electron spherical quantum dot-quantum well structure consisting of a CdSe core surrounded by ZnS and CdSe shells and capped by material with a higher electron potential barrier compared with CdSe is investigated. Eigenfunctions and corresponding energies are calculated using effective mass approximation. For allowed transitions between ground and three excited states (1s, 2p, 3d, and 2s), we have calculated dipole transition matrix elements and linear and third-order nonlinear intersubband refractive index changes for different CdSe core radii and ZnS and CdSe shells thicknesses. Electron wave functions and energy of states are considerably affected by the dimensions of core and shells. The localization regime of electron in 1s, 1p, 1d, and 2s states and hence transition energies and dipole matrix elements of 1s-1p, 1p-1d, and 1p-2s transitions can be controlled by core and shell dimensions.