In this paper, the dynamic model of the rigid space stepped-pipe strings system is derived with Lagrangian method to represent the system dynamic behaviors which enriches the analysis method of longitudinal vibration of stepped-pipe strings. The stepped-pipe strings is constructed of pipes with different diameters and lengths, the physical properties of which mainly depends on the axial force and the depth of deep-sea mining. Based on lumped element method, the heave compensation system with dynamic vibration absorber is designed for longitudinal vibration suppression of the stepped-pipe strings. The analytical solution is obtained by modal analysis method when the mining ship is subjected to sea breeze excitation. The proposed method is easily implementable for rigid space stepped-pipe strings system with complex multi-degree-of-free deep-sea mining dynamic model. Furthermore, the optimal combination of mass ratio, spring coefficient and damping ratio is shown to have a better vibration suppression performance. Finally, numerical simulations on the stepped-pipe strings system with or without dynamic vibration absorbers are provided to demonstrate the effectiveness of the proposed method.