  High-pressure properties of MnPS$_3$ are investigated by using the hybrid
functional, we report a spin-crossover pressure of 35 GPa consisting with
experimental observation (30 GPa), less than half of existing report (63 GPa)
using the Hubbard U correction. Interestingly, a spin-crossover induced
antiferromagnetism-to-ferromagnetism transition combined with stacking-order
change from monoclinic to rhombohedral are founded, and the ferromagnetism
origins from the partially occupied $t_{2g}$ orbitals. Different from previous
understanding, the Mott metal-insulator transition of MnPS$_3$ does not occur
simultaneously with the spin-crossover but in pressurized low-spin phase.
