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In CNFETs, the Drain Induced Barrier Lowing (DIBL) effect is still a primitive problem and open for further study. Based on a numerical model developed with the Non-Equilibrium Green's Function (NEGF) approach in real space, this paper studied the DIBL effect in Carbon Nanotube-FETs (CNFETs). Some interesting phenomena of the impact of DIBL on the energy band have been noticed. For example, the relationship between the degree of barrier lowing and the drain-source voltage is not linear but of a step-like quantization, and the energy band shape (gradient or aclinic) is closely related to Fermi-level. For the first time, a detailed explanation of the underlying physical mechanism of the observed DIBL effect is presented according to the electronic structure, the effective capacitance model and the quantum capacitance model of CNFETs. Then the correlation between DIBL effect and the insulator thickness, insulator dielectric constant, CNT diameter and channel length is studied. At the end, a conclusion is made by summarizing the differences between the DIBL effect in CNFETs and that in short channel MOSFETs, and several approaches is presented to reduce the leakage current resulting from the DIBL effect.