The electronic structure of the MgH molecule is investigated using a pseudopotential description of the Mg2+ core, complemented by a core polarization operator. The electronic problem is treated by the Internally Contracted Multi-Reference Configuration Interaction method (IC-MRCI). The potential energy curves and the molecular constants are calculated for all MgH molecular states dissociating up to the excited atomic configurations Mg(3s3d(1)D) + H(1s(2)S). A good agreement with the available experimental data is found. These calculations help to clarify the very complicated spectroscopy of MgH in the 3500046000 cm(-1) excitation range, where many states correlated with the 3s3p, 3s4s and 3s3d atomic configurations cross one another. For instance, the predissociation mechanism of the B-2 Sigma(1) state is enlighten. Both the doublet and quartet systems are documented.