Cylindrical structures in many engineering constructions are used, so proper analysis of cylinder behavior under various conditions is important. In this paper we investigate the dynamic and vibrational response of carbon nanotube-reinforced carbon nanotube reinforced composite cylinder shell with two piezoelectric layers. The equations of motion are extracted by assuming Sanders shell theory using the Hamiltonian principle. The Quadrature Differential Method (DQM) is used to solve the equations of motion. Frequency changes and dynamic response (middle layer displacement) have been studied by varying geometric and piezoelectric parameters. Among piezoelectric parameters, the parameter of C11 has a lower effect than the effective transverse coefficient of e31 in the frequency response. Other piezoelectric parameters have very little effect on frequency. A mild initial heat field increases the displacement amplitude by decreasing the strength and brittle of the material. But the heat field reduces the hardness of the matrix to a greater extent and increases the frequency and amplitude of the displacement.