Abstract: The properties of polaron in the nanotubes are studied by using a combination of precisely solving the energy eigen-equation, unitary transformation and variation method. Numerical calculation results indicate that the energy of ground state and the first excited state of polaron in the nanotubes increase with increasing nanotube inside radius (or decreasing nanotube outside radius) , which illustrates that the nanotube has obvious quantum size effect. Numerical results also show that energies mentioned earlier low when the effect of phonon is taken into account, because the interaction between the electron and phonons leads to the absolute value of the interaction energy between them increasing, resulting polaron energy going down. It is also found from numerical results that the energy of ground state and the first excited state of polaron increase with increasing wave vector along the nanotube orientation, because of increasing wave vector, leading to the kinetic energy of the electron and the energy of polaron increase.