Here, we report a new intrinsic magnetic topological insulator FeBi2Te4 based on first-principles calculations and it can achieve a rich topological phase under pressure modulation. In the absence of pressure, we predict that both FeBi2Te4 ferromagnetic and antiferromagnetic orders are non-trivial topological insulators. Furthermore, FeBi2Te4 of FM-z ordering will undergo a series of phase transitions from topological insulator to semimetals and then to trivial insulator under pressure. Finally, we further clarify and verify the fact of topological phase transitions in conjunction with low-energy effective model calculations. This topological phase transition process is attributed to the synergy of the magnetic moment and the spin-orbit coupling. The unique topological properties of FeBi2Te4 will be of great interest in driving the development of quantum effects.