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A variational calculation is presented for the ground-state properties of excitons confined in spherical core-shell quantum-dot quantum-well (QDQW) nanoparticles. The relationship between the exciton states and structure parameters of QDQW nanoparticles is investigated, in which both the heavy-hole and the light-hole exciton states are considered. The results show that the confinement energies of the electron and hole states and the exciton binding energies depend sensitively on the well width and core radius of the QDQW structure. A detailed comparison between the heavy-hole and light-hole exciton states is given. Excellent agreement is found between experimental results and our calculated 1se-1sh transition energies.