In this paper, an L-shaped tunneling field effect transistor (LTFET) with ferroelectric gate oxide layer (Si: HfO2) is proposed. The electric characteristic of NC-LTFET is analyzed using Synopsys Sentaurus TCAD. Compared with the conventional LTFET, a steeper subthreshold swing (SS = 18.4 mV/dec) of NC-LTFET is obtained by the mechanism of line tunneling at low gate voltage instead of diagonal tunneling, which is caused by the non-uniform voltage across the gate oxide layer. In addition, we report the polarization gradient effect in a negative capacitance TFET for the first time. It is noted that the polarization gradient effect should not be ignored in TFET. When the polarization gradient parameter g grows larger, the dominant tunneling mechanism that affects the SS is the diagonal tunneling. The on-state current (Ion) and SS of NC-LTFET become worse.