With first-principle calculations, we investigate elastic and magneto-optical properties of Al₁₄Mn₂P₁₆ under hydrostatic pressures (0~20 GPa). Our calculations show that the ground state is a ferromagnetic state. The system was proved stable according to the elastic stability criterion. The magnetic moment decreases with increasing hydrostatic pressure. Below 5 GPa, the system hosts Curie temperature (T_C) of 184 K combine with a slightly decrease with increasing hydrostatic pressure. Furthermore, intriguingly, as external pressure furthers improves, T_C drops sharply, even vanishes at 18 GPa. It was found that the absorption peak in visible optical range has obvious blue shift. As hydrostatic pressure reaches 20 GPa, absorption peak in visible optical range disappears.