PbTiO₃ (PTO) is an important ferroelectric functional material, but its structure, stability, mechanical property, and thermodynamic property under pressure is still unknown, leading to restriction in applying in the field of electronic communication. Here, first-principles calculations based on density functional theory was performed to study the structure and thermal properties of pre-perovskite phase PbTiO₃ (PP-PTO), ferroelectric tetragonal phase PbTiO₃ (TP-PTO), and paraelectric cubic phase PbTiO₃ (CP-PTO) under pressure. It is found that their compressibility in descending order is PP-PTO>TP-PTO>CP-PTO. Under considered pressure, three PTO phases have not undergone a phase transition analyzed by band structure and density of states, and their band gap gradually decreases with increasing pressure. Among them, the TP-PTO changes from an indirect to a direct band gap semiconductor at 20 GPa, while the others remain a direct band gap semiconductor. Those PTO phases are mechanically stable and anisotropy from 0 to 30 GPa. Furthermore, their comprehensive mechanical properties increase and anisotropy firstly decreases and then increases with increasing pressure. Analysis based on quasi- harmonic Debye approximation theory was performed to study the influence of temperature and pressure on Debye temperature, entropy and heat capacity. The results illuminate that Debye temperature decreases with temperature increase, nevertheless, pressure has the opposite effect, which elucidates that the order of covalent bond from strong to weak is CP-PTO>TP-PTO>PP-PTO. Entropy and heat capacity of PTO increase with rising temperature, but decrease with the increase of pressure.