In this work, we aim a detailed investigation of the electronic properties of a spherical multi-layer quantum dot with and without a hydrogenic impurity. The structure is introduced in the form of core/shell/well/shell layers. The core and well layers are defined by the parabolic electronic potentials. We carry out the effect of the core radius and layer thickness on the energy levels, their wave functions, binding energies of the impurity and the probability distributions. In order to determine the sublevel eigenvalues and eigenfunctions, the Schrodinger equation is solved full numerically by shooting method in the frame of the effective mass approximation. The results are analyzed in detail as a function of the layer thicknesses and their probable physical reasons are tried to be explained. It is found that the electronic properties and impurity binding energies are strongly depending on the layer thicknesses. (C) 2012 Elsevier B.V. All rights reserved.