Carbon nanotube (CNT) could be exploited as a channel or source/drain region in field effect transistors (FETs). We theoretically investigate the impact of Source and Drain doping level on a coaxially gated CNTFET's performance in the ballistic regime. The results show that the On/Off Ratio, Subthreshold swing, Cutoff Frequency, transconductance and delay are improved with choosing the source and drain doping structure. It seems that the most important impact of Source and Drain doping level and length is the reason of change and shift in the transfer characteristics of the device simulation results values. However, form this paper it is possible to choose an optimal value of CNTFET Gate voltage and gate length to obtain better performance.