We have performed a theoretical study of the exciton properties in the CdxZn1-xS/ZnS quantum wells (QWs) with taking into account the strain effect due to a ZnS buffer layer. The variation of the exciton binding energy that is caused by the strain effect due to the ZnS buffer layer is very small. The variation of the effective band gap energy is larger than that of the exciton binding energy under the strain due to the ZnS buffer layer. The effect of the electric field on the exciton binding energy is calculated using a variational approach. The exciton binding energy decreases with increasing the electric field, and decreases significantly at the wide well widths due to the spatial separation between the electron and the hole. The diamagnetic shift of the exciton is calculated under the magnetic field, and is less than 0.11 meV.