On the basis of optimized geometric structure at B3LYP/6-31G level, the energy gaps, E, of three types of short armchair carbon nanotubes with various lengths have been calculated at PM3 and also B3LYP/6-31G levels, respectively. The results found that a regular oscillation with period 3a/2 appeared on the Eg, and the E, are reduced gradually and have the least at N-s = 3ma/2 along with increasing the tube length N-s. The E-g calculated values are also consistent with those reckoned from STM and AFM experiments. The theoretical simulated method developed in this Letter reproduced successfully the results obtained from above-mentioned complicated calculations and SPM technique. The simulated method proved that the periodic boundary condition is also suitable for the axial direction of short armchair nanotubes but then the variation Deltak induced by finite tube length must be considered. According to the modified boundary condition, an unified condition suited to the vectors of carbon nanotube axial and its radial directions was obtained and the essence correlated with E-g periodic variance was revealed. (C) 2002 Published by Elsevier Science B.V.