Utilizing γ-graphyne-1 nanotubes (GyNTs) in the Tunneling Field Effect Transistors (TFETs) suppresses ambipolarity and enhances subthreshold swing (SS) of TFETs which is because of large energy band gap and high electron effective mass of GyNTs. In this research analysis of structural, electronic and thermoelectric properties of γ-graphyne-1 family under the deformation potential (DP) approach reveals that electron-phonon mean free path (MFP) of an Armchair GyNT (3AGyNT) and Zigzag GyNT (2ZGyNT) are 45 and 290 nm, respectively. Therefore, ballistic transport of sub 10 nm 3AGyNT-TFETs and 2ZGyNT-TFETs in different channel lengths are investigated utilizing Non-Equilibrium Green's Function (NEGF) formalism in the DFTB platform. Ultrahigh Current Ratio (OOCR) value of 1.6 x 10 10 at V DD = 0.2 V and very low point SS of 5 mV/dec are belonged to the 3AGyNT-TFET with channel length of 9.6 nm. 2ZGyNT-TFETs shows higher on-state current and SS as well as lower OOCR than those of 3AGyNT-TFETs. A linear relationship between channel length and logarithmic off-state current is reported that is consistent with WKB approximation. The obtained results along with the ultralow power consumption of the suggested GyNT-TFETs, make them as replacement of digital silicon MOSFETs in the next generation nanoelectronic devices.