A novel line tunneling based gate-on-source-only tunnel field-effect transistor (TFET) with inverted T-shaped channel (ITGOSO-VTFET) is proposed and investigated using a Synopsis TCAD 2-D simulator. The GOSO configuration along with dual counter-doped pockets (CDP) improve the ON-state current by enhancing the tunneling rate of charge carriers at source/channel interface while inverted T-shaped channel helps the proposed device in reducing the OFF-state (I_OFF) and ambipolar (I_AMB) currents. In comparison with double-gate (DG) and GoSo-CDP TFET, the order of I_OFF (I_AMB) in ITGOSO-VTFET are found to be improved by ~6 (~4) and ~7(~3), respectively. Furthermore, the impact of varying design parameters is analyzed to obtain the optimized performance of the proposed device. Apart from improvement in DC performance, ITGOSO-VTFET is also found to offering a much better analog/radio-frequency performance in terms of various parameters like g_m, f_T, TFP, GBP, and τ, which eventually makes the proposed device more suitable for low power and high-speed applications