Using a variational method with introduction of effective electron potentials, binding energies and overlap functions of exciton ground states in ZnSe/ZnS quantum dots (QDs) with small conduction-band offset are calculated. It is found that excitons in ZnSe/ZnS QDs are incompletely confined due to the extension of electrons in the weak confinement condition. The binding energies of such excitons are almost independent of potential shapes and quantum sizes while the overlap functions are dependent on the shapes and sizes of QDs. It is quite different between ZnSe/ZnS and conventional QDs and this will be subjected to experimental verification in the future.