The properties of polaron in nanotubes are invesgated by combination of solving the energy eigen-equation, unitary transformation and variation method. Numerical calculation results indicate that the energy of ground state and first excited state of polaron increases with increasing nanotube inside radius or decreasing nanotube outside radius, which illustrates that the nanotubes have obvious quantum size effect. It decreases with increasing of the electron-phonon coupling strength. The interaction between the electron and phonon leads to the absolute value increasing of interaction energy and decreasing of the polaron energy. It increases with increasing wave vector along the nanotube orientation. Increasing wave vector of the direction leads to increasing of the electron kinetic energy, and the energy of polaron increases.