The pressure-induced phase transitions of MoAlB have been fully studied to provide insights into the typical MAB phases under high pressure. A novel high-pressure monoclinic structure (C2/m, Z = 4) was firstly identified for the MoAlB above 234 GPa, using the first principles crystal structure prediction approach. First-order structure transition character of MoAlB from the ambient-pressure orthorhombic Cmcm phase to this high-pressure monoclinic C2/m phase was demonstrated by a volume drop of 1.28%. Inspections of crystal structures showed that the occurrence of C2/m phase follows the slip in the metallic Al-Al layers and the fracture of linear zigzag B-B chains in the Cmcm phase under compression, confirming the earlier reports. Our argument has been also supported by the softening of elastic constant under high pressure. Phonon curves calculations suggest the high-pressure C2/m phase can be quenchable to ambient pressure. The electronic and mechanical properties of this novel C2/m phase have thus been systematically investigated.