With the development of semiconductor technology, the size of traditional metal oxide semiconductor field effect transistor devices continues to decrease, but it cannot meet the requirements of high performance and low power consumption. Low power tunneling field effect transistor (TFET) has gradually become the focus of researchers. This paper proposes a novel T-shaped gate TFET based on the silicon with the negative capacitance (NC-TGTFET). On the basis of TGTFET, ferroelectric material (HZO) is used as gate dielectric. The simulation results show that, compared with the traditional TGTFET, the opening order and sensitivity of the two tunneling junctions are different. The influences of thickness and the doping concentration of pocket and ferroelectric material properties on the characteristics of NC-TGTFET is also discussed by Sentaurus simulation tool. Furthermore, the negative capacitance of ferroelectric material makes NC-TGTFET have a very steep subthreshold swing (18.32 mV/dec) at the range of drain current from 1 × 10−15 to 1 × 10−7 A μm−1. And the on-state current (V g = 0.5 V, V d = 0.5 V) is 1.52 × 10−6 A μm−1.