The equilibrium geometries of three electronic states X2Σ+，A2Π and B2Σ+ of MgH molecule have been calculated using the SAC-CI and QCISD (T) methods with the basis sets cc-pVQZ，aug-cc-pVTZ，6-311++G and 6-311++G(3df，2pd). Comparing the above mentioned four basis sets，the conclusion is obtained that the basis set 6-311++G (3df，2pd) is the most suitable for the energy calculation of MgH molecule. The whole potential curves for three electronic states are further scanned using QCISD (T)/6-311++G (3df，2pd) method for the ground state and SAC-CI/6-311++G (3df，2pd) method for the excited states. The potential energy functions and relevant spectrum constants ωe，ωexe，Be，αe of these states are obtained by fitting to the Murrell-Sorbie function and the modified Murrell-Sorbie+C6 function，respectively. The results showed that the spectral constants derived from the modified Murrell-Sorbie+C6 function are in very good agreement with the experimental data，and the modified Murrell-Sorbie+C6 function can correctly describe the potential energy function of the ground state and the first degenerate state of MgH molecule.