The influence of external pressure on the structural properties of manganese monophosphides (MnP) at room temperature has been studied using in situ angle dispersive synchrotron x-ray powder diffraction (AD-XRD) with a diamond anvil cell. The crystal structure of MnP is stable between 0 to 15 GPa. However, the compressibility of b-axis is much larger than those of a- and c-axes. From this result we suggested that the occurrence of superconductivity in MnP was induced by suppression of the long-range antiferromagnetically ordered state rather than a structural phase transition. Furthermore, the present experimental results show that the Pnma phase of MnP undergoes a pressure-induced structural phase transition at ~15.0 GPa. This finding lighted up-to-date understanding of the common prototype B31 structure (Strukturbericht Designation: B31) in transition metal monophosphides. No additional structural phase transition was observed up to 35.1 GPa (Run 1) and 40.2 GPa (Run 2) from the present AD-XRD results. With an extensive crystal structure searching and ab initio calculations, we predict that MnP underwent two pressure-induced structural phase transitions of Pnma → P213 and P213 → Pm-3m (CsCl-type) at 55.0 and 92.0 GPa, respectively. The structural stability and the electronic structures of manganese monophosphides under high pressure are also briefly discussed.