The assembly of single-walled carbon nanotubes (SWCNTs) using the AC dielectrophoresis technique is studied theoretically. It is found that the comb electrode bears better position control of SWCNTs compared to the parallel electrode. In the assembly, when some SWCNTs bridge the electrode first, they can greatly alter the local electrical field so as to "screen off" later coming SWCNTs, which contributes to the formation of dispersed SWCNT array. The screening distance scales with the gap width of electrodes and the length of SWCNTs, which provides a way to estimate the assembled density of SWCNTs. The influence of thermal noise on SWCNTs alignment is also analyzed in the simulation. It is shown that the status of the array distribution for SWCNTs is decided by the competition between the thermal noise and the AC electric-field strength. This influence of the thermal noise can be suppressed by using higher AC voltage to assemble the SWCNTs.