We report the transition of a strain-induced centrosymmetric β-phase to a non-centrosymmetric α-phase for monolayer tellurene based on density functional theory calculations. The phase transition is represented by the displacement of the middle-layer Te atoms from the center of the unit cell in the y-direction. The critical point for the phase transition is found to be at 0.5% biaxial tensile strain. By analyzing the bond variation and the phonon spectra, we attribute the phase transition to the decrease of the bonding strength at the tensile strain and the atom migration corresponding to the phonon vibration mode along the distorted direction. The transition to the α-phase under strain is further confirmed from the calculated electronic band structure where the spin-orbit coupling (SOC) induces a large Rashba splitting due to symmetry breaking, which may enable the control of spin via the electric field. Two-dimensional ferroelectrics can be formed upon transition of the strain-induced β-phase to the α-phase, and a high polarization of about 90 μC cm-2 can be achieved via a tensile strain, giving rise to a giant piezoelectric coefficient that is two orders of magnitude higher than that of the MoS2 monolayer.