For the first time, an asymmetric lightly doped Schottky barrier carbon nanotube field effect transistor (SB_CNTFETs) is proposed and simulated using quantum simulations. Comparisons are made among four SB_CNTFETs structures for electrical characteristics. One is the conventional SB_CNTFET with an intrinsic channel. The other proposed and studied designations are an asymmetrically doped SB_CNTFET with a doped region near the source only, a symmetrically doped source and drain SB_CNTFETand an asymmetric lightly doped SB_CNTFET which shows the ultimate performance among all. The results show that the new asymmetric lightly doped design decreases significantly the leakage current and thus increases on/off ratio as well as cutoff frequency. It is also demonstrated that this structure possesses two perceivable steps in potential profile of the channel, which lead to another lateral electric field peak inside the channel which leads to the immunity against short-channel effects. The cutoff frequency characteristics of the four structures of SB_CNTFETs have been discussed. Results show that for channel lengths >30 nm cutoff frequency of the asymmetric lightly doped SB_CNTFETis greater than others. The effect of different doped region lengths in a 30 nm SB_CNTFET has been discussed as well. The proposed new design is promising from several points of view discussed in the study.