An eigen-equation method under tight binding approximation is developed to find the plasmon of two-dimensional quantum dots. The results show that the plasmon charges may show monopolar, dipolar, or quadrupolar polariztion in the transverse or longitudinal direction, respectively, which may localize at the center, end, or boundary of quantum dots. According to the charge-polarization and charge-localization characteristics, it is assumed that there exist 24 or 27 plasmon modes in a two-dimensional uncharged or charged system, respectively. In addition, the size effect of various plasmon modes may differ, e.g., the plasmon frequency of the monopole-dipole end mode shifts towards the red end of the spectrum as the longitudinal size increases. In contrast, the frequency of the dipole-monopole end mode shifts towards the blue end of the spectrum as the longitudinal size increases.