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In spite of recent findings about the pressure-driven insulator-to-metal phase transition, and emerging superconductivity of FePS₃ and FePSe₃, the knowledge about the atomic structures of them is still vague. Here, we investigate the pressure-driven structural phase transitions of FePS₃ and FePSe₃ from 0 to 35 GPa by using ab initio calculations. We find that FePS₃ B-I structure transforms to FePS₃ B-II phase at about 5 GPa. Then above 17 GPa, FePS₃ B-III phase becomes energetically favored. For FePSe₃, with increasing pressure, FePSe₃ transforms to B-II phase at around 6 GPa and further to B-III phase at about 15 GPa. Our calculation results are consistent with experimentally observed high-pressure induced cell volume collapse, spin-crossovers and insulator-metal transition in FePS₃ and FePSe₃, which shed new light on understanding the high-pressure physics and phase transitions of FePS₃ and FePSe₃.