Using the band gap properties of the periodic structure, the truss structure of an offshore platform is designed as a one-dimensional periodic conduit structure, and the band gap characteristics are used to realize the vibration control of the truss structure of the offshore platform. The finite element method is used to simulate the vibration characteristics of the periodic conduit, and the influence of the structural parameters (length and wall thickness) of the periodic conduit on the vibration band gap of the periodic conduit is analysed. The frequency response characteristics of the periodic truss structure of an ocean platform are calculated and compared with those of a traditional truss structure. The results show that the periodic truss exhibits better suppression of vibration transmission than the traditional truss, especially for the vibration in the band gap, which is greatly attenuated. This study shows that the periodic structure has broad application prospects in vibration isolation design of truss structures for offshore platforms. The research provides a new technical approach for vibration control of truss structures on offshore platforms.