Stress induced phase transformation from hexagonal close-packed titanium (HCP-Ti) to face-centered cubic titanium (FCC-Ti) is believed to be a reason for the pronounced work hardening of carbon nanotube-reinforced titanium (CNT/Ti) composites prepared by high-pressure torsion (HPT). Here, the correlation between the phase transformation from the HCP-Ti to the FCC-Ti structure in Ti and the improved mechanical properties of CNT/Ti composite is revealed by investigating the structural transformation mechanism, the stability, electronic properties, anisotropic elasticity and thermodynamics of the FCC-Ti and HCP-Ti crystals under pressure of 0-15GPa by means of first-principles calculations and comparing with the experimental findings. The results show that the formation enthalpies δHTi, the bulk modulus B, the shear modulus G and the Young's modulus E of the FCC-Ti and HCP-Ti structures gradually increase with increasing pressure, and the hybridization between the electronic orbitals of the atoms becomes stronger. The Young's modulus of the cubic FCC-Ti structure shows strong anisotropy along the [0 1 0] and [1 10] directions, while the HCP-Ti structure exhibits an obvious anisotropy of E in the (1 0 0) crystal plane. The thermodynamic stability of the HCP-Ti and FCC-Ti structures decreases under high pressure. The different relative stability of the two structures results in a high propensity of structural transformation from the HCP-Ti to the FCC-Ti structure. A large number of FCC-Ti structures are prepared, which can effectively improve the mechanical properties of CNT/Ti composites. Our results may help to better understand the phase transition from HCP-Ti to FCC-Ti under high pressure, and may reveal the structure-property relationship of CNT/Ti composites.