The change rules of electronic structure and magnetism in the process of transform from a cubic structure to a tetragonal structure and their responses to pressure for Hg2CuTi-type Mn2NiAl are studied by first principles method based on the density functional theory. The study shows that in the process of transform from a cubic austenite phase to a tetragonal martensite phase, the shift of the density of states of occupied state to ward lower energy in the martensitic phase results from the enhanced Ni-Mn(A) hybridization caused by a decrease in the Ni-Mn(A) distance, and it is the reason for the stabilization of the martensitic phase. In the process of transform from the austenite phase to the martensite phase, the bonding interaction becomes stronger, owing to energy band broadening, and it can improve the stabilization in the martensitic phase. In the process of tetragonal distortions, the change of total magnetic moment is determined by the change of magnetic moment of Ni atom. The bulk modulus at zero pressure of Mn2NiAl is calculated to be 125.69 GPa, so that we expect Mn2NiAl to be the more compressible material than the familiar Heusler alloys.