Piezotronics and piezophototronics are emerging fields by coupling piezoelectric, semiconductor, and photon excitation effects for achieving high-performance strain-gated sensors, LEDs, and solar cells. The built-in piezoelectric potential effectively controls carrier transport characteristics in piezoelectric semiconductor materials, such as ZnO, GaN, InN, CdS, and monolayer MoS2. In this paper, a topological insulator piezotronic transistor is investigated theoretically based on a HgTe/CdTe quantum well. The conductance, ON/OFF ratio, and density of states have been studied at various strains for the topological insulator piezotronic transistor. The ON/OFF ratio of conductance can reach up to 1010 with applied strain. The properties of the topological insulator are modulated by piezoelectric potential, which is the result of the piezotronic effect on quantum states. The principle provides a method for developing high-performance piezotronic devices based on a topological insulator.