We present the behaviors of both dynamical and static charge susceptibilities of doped armchair nanotubes using the Green function approach in the context of Holstein-model Hamiltonian. Specially, the effects of magnetization and gap parameter on the the plasmon modes of armchair nanotube are investigated via calculating correlation function of charge density operators. Random phase approximation has been implemented to find the interacting dynamical charge susceptibility. The electrons in this systems interacts with each other by mediation of dispersionless Holstein phonons. Our results show that the increase of gap parameter leads to decreasing intensity of charge collective mode. Also the frequency position of the collective mode tends to higher frequencies due to the gap parameter. Furthermore the number of collective excitation mode decreases with chemical potential in the presence of electron–phonon interaction. Finally the temperature dependence of static charge structure factor of armchair nanotubes is studied. The effects of the gap parameter, magnetization and electron–phonon interaction on the static structure factor are addressed in details.