Based on the effective-mass approximation, the energy spectrum of the free A-exciton states of cadmium sulphide is studied. The Stark effect in an electric field, the Zeeman effect and the diamagnetic interaction in a magnetic field of the A-exciton states are analysed by using a novel perturbative-variational approach. The results are compared with experimental data and previous calculations using different approaches. Results are in good agreement with previous work and the method is much more efficient.