Based on the relativistic theory, the wavefunctions and low-lying levels of highly charged states of hydrogen-like ions for the shells n=1—3 were calculated using different nuclear models——point-like nuclear and Fermi nuclear models with two parameters, respectively. The influence of the finite nuclear size on wavefunctions and level energies were analysed. Furthermore, a fitting formula related to nuclear parameter a and c in Fermi nuclear model for finite nuclear effects on the atomic level energy is deduced. The mutual influence between the relativistic effect and the finite nuclear size effects were discussed. It is found that there is a strong coupling between relativistic effect and finite nuclear size effects for high-Z elements.