The reason of the emergence of longitudinal modes in the single-mode slow-wave structure(SWS) is analyzed in terms of the transmission line theory, which proves that the occurrence of the longitudinal modes can be attributed to the unmatchi ng between the impedance of the SWS and that of its input and output ends. With the method of S-parameter, the features, such as frequency, field distributi on and the Q-factor of the longitudinal modes of TM01 mode in the over moded SWS are investigated, and the influence of the period-number of the SWS on the number, the frequency interval and the Q-factor of longitudinal modes a re analyzed. It is proposed that the introduction of a well designed resonant ca vity to O-type HPM devices can help to achieve the longitudinal mode selection a nd reduce the period-number of the SWS, which not only can make the devices more compact, but also can avoid the destructive competition between various longitu dinal modes, therefore can enhance the efficiency and stabilize the frequency.