In this paper, we propose a new type of tri-input tunneling field-effect transistor (Ti-TFET) that can compactly realize the “Majority-Not” logic function with a single transistor. It features an ingenious T-shaped channel and three independent-biasing gates deposited and patterned on its left, right, and upper sides, which greatly enhance the electrostatic control ability between any two gates of all the three gates on the device channel and thus increase its turn-on current. The total current density and energy band distribution in different biasing conditions are analyzed in detail by TCAD simulations. The turn-on current, leakage current, and ratio of turn-on/off current are optimized by choosing appropriate work function and body thickness. TCAD simulation results verify the expected characteristics of the proposed Ti-TFETs in different working states. Ti-TFETs can flexibly be used to implement a logic circuit with a compact style and thus reduce the number of transistors and stack height of the circuits. It provides a new technique to reduce the chip area and power consumption by saving the number of transistors.