By using the tight-binding model and the eigen-equation method, both the dipole and quadrupole modes of the plasmon in one-dimensional system are studied. The modulation effects of the external field, the size of system and the number of electrons on these two modes are investigated. The results show that, the modes of the plasmon can be controlled by the external field, a symmetrical electric potential field only excites the quadrupole mode, and an anti-symmetrical electric potential field only excites the dipole mode. Based on the size effect of plasmon, the increase of the length of one-dimensional system can reduce the plasmon frequency and enhance the excitation intensity. Based on the charge accumulation effect of plasmon, the increase of the number of electrons before half filling can increase the frequency and excitation intensity of plasmon. Moreover, the excitation intensity of plasmon is symmetric with respect to the half-filling electron number since the excitations of electrons and holes are equivalent. As for the size effect of plasmon, the results calculated by the eigen-equation method can be well fitted by those obtained by the random phase approximation method.