In this paper, both linear and third-order nonlinear optical properties of two-electron in a semiconductor core/shell/well/shell quantum dot (QD) heterostructure for cases with and without a hydrogenic donor impurity have been investigated in a detailed manner as depending on the structure parameters. For this purpose, first, the energy eigenvalues and corresponding wave functions of the structure have been computed as a function of the layer thicknesses by means of the self-consistent solution of the Poisson and Schrodinger equations in envelope function effective mass approximation. Second, using these energy eigenvalues and their wave functions obtained from the calculations, both linear and third-order nonlinear optical properties of the multi-shell QD (MSQD) with two-electron have been determined as a function of the photon energies and shell thicknesses. Also, all procedures mentioned above have been repeated for negatively charged donor impurity (D-) located in the center of the same structure. Finally, obtained results have been presented comparatively for cases with and without the impurity. (C) 2015 Elsevier Ltd. All rights reserved.