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Full complex band structure-based NEGF simulation results of the subthreshold leakage characteristics of nano-scale carbon nanotube field-effect transistors (CNTFETs) are provided. These results show qualitatively unconventional subthreshold behavior, which needs to be considered for the scaling of CNTFETs. To fully understand the subthreshold current of nanoscale channel length CNTFETs, tunneling-mediated leakage currents must be considered. And for narrow-gap CNTs, the proximity of the electron tunneling path to the valence band as well as the conduction band should be considered; that is, a simple effective mass approximation is not reliable. In this work, we address the transport behavior of a nanoscale CNTFET with zigzag nanotubes, using the NEGF method with a full-band tight-binding model, including the complex bandstructure effect by the bandgap states of CNTs.