The methylammonium lead iodide (CH3NH3PbI3) perovskite is a new type of photovoltaic material, which has attracted widespread attention due to its excellent photoelectric properties. Here, the mechanical properties and structural stability of five phases of CH3NH3PbI3 under high pressure are studied using first-principles. These works help to improve the understanding of CH3NH3PbI3 and predict the new structure. The results show that the two hexagonal phases transform to orthorhombic phase at 1.0 GPa and 2.0 GPa, respectively. The tetragonal phase transforms to cubic phase at 0.3 GPa. Furthermore, in the 2H-phase, Young’s modulus (E) decreases with increasing pressure, which means that stiffness decreases with increasing pressure. However, in orthorhombic, tetragonal, and cubic phases, as the pressure increases, E first increases and then decreases. The Pugh’s ductility index (G/B) of 2H-phase is greater than 0.57and the one of T-phase is less than 0.57, which proves that the 2H-phase is brittle and the T-phase is tough. The Pugh’s ductility index of the other three phases changes around 0.57 with the increase of pressure. As the increase of pressure, only the elastic constant of 4H-phase cannot meet the mechanical stability criteria, and the other four phases can meet.