To utilize the interaction between the field and the electron beam in a traveling wave tube （TWT）, the velocity of electrons and the longitudinal phase velocity of field should be made approximately equal. But when the electromagnetic energy increases, the electrons are slowed down and the synchronization condition is no longer satisfied in periodic structures. However, the varying-period slow-wave structure can be used to maintain the synchronization in the whole interaction section. This structure also has the advantages of space harmonic selectivity and wide bandwidth. The space harmonic in varying-period slow-wave structures is analyzed here. The synchronization condition of one space harmonic with the electron beam during the whole interaction process is presented in this paper. And the folded waveguide with varying period is analyzed as an example.