In this paper, the plasmon-induced transparency (PIT) effect based on a carbon nanotube (CNT) resonator structure is achieved. An array of two split ring resonators (SRRs) and a cut wire (CW) resonator are utilized to form the proposed metamaterial. A PIT transparency window is achieved under a TM polarization terahertz light. Results show that the PIT effect is originated from the near-field coupled of the bright mode and dark mode. A coupled harmonic oscillator model is used to describe the near-field coupling between the bright mode and subradiant mode, and the results agree well with the FDTD simulation. The effect of geometrical sizes, like structure period, the radius and the splitting degree of the split ring resonator, the length of the cut wire resonator, and the coupling distance on the PIT window is analyzed in detail. Besides, the sensing and slow light performance of the proposed CNT metamaterial are studied, a maximum sensitivity of 0.74 THz RIU, and a time delay of 0.54 ps are obtained. Therefore, the proposed CNT-based device can be applied to the PIT effect, near-infrared modulators, slow light devices, sensors, and other fields.