This paper reports the density of states (DOS) of chiral (4,1), armchair (4,4), and zigzag ((4,0) single-walled carbon nanotubes (SWCNTs) by using ab-initio Density Functional Theory (DFT). Our simulation results show the distinguishable features of three types of CNTs in terms of density of states (DOS), so that they can be fully exploited in nano-devices. The results are helpful for studying the working principles of the CNT-based electronic devices and designing new ones.