Abstract A periodic vibration suppressor with multiple secondary oscillators is examined in this paper to reduce the low-frequency vibration. The band-gap properties of infinite periodic structure and vibration transmission properties of finite periodic structure attached with secondary oscillators with arbitrary degree of freedom are thoroughly analyzed by the plane-wave-expansion method. A simply supported plate with a periodic rectangular array of vibration suppressors is considered. The dynamic model of this periodic structure is established and the equation of harmonic vibration response is theoretically derived and numerically examined. Compared with the simply supported plate without attached suppressors, the proposed plate can obtain better vibration control, and the vibration response can be effectively reduced in several frequency bands owing to the multiple band-gap property. By analyzing the modal properties of the periodic vibration suppressors, the relationship between modal frequencies and the parameters of spring stiffness and mass is established. With the numerical results, the design guidance of the locally resonant structure with multiple secondary oscillators is proposed to provide practical guidance for application. Finally, a practical periodic specimen is designed and fabricated, and then an experiment is carried out to validate the effectiveness of periodic suppressors in the reality. The results show that the experimental band gaps have a good coincidence with those in the theoretical model, and the low-frequency vibration of the plate with periodic suppressors can be effectively reduced in the tuned band gaps. Both the theoretical results and experimental results prove that the design method is effective and the structure with periodic suppressors has a promising application in engineering.