Subject to the limited envelope size and carrying capacity of a rocket, it could be one of the most promising solutions to construct a large space structure through multilaunching and on-orbit assembly. Taking the antenna of the solar power satellite as the research objective, a novel vibration suppression strategy is developed in this article to guarantee high structural stability of the large space structure during on-orbit assembly. The concept of distributed control unit, together with the varying location relationship matrices, reflects the structural characteristics of the large space structure during on-orbit assembly. The explicit expression form of the control unit’s dynamic model is first derived based on the Newmark-β method. Then, the distributed adaptive model predictive controller is proposed to suppress the vibration of the large space structure aroused by weak impact among assembling modules. Through recalculating the control matrices efficiently at each assembly, the proposed controller achieves adaptive updating along with the varying large space structure. The feasibility of the proposed distributed adaptive model predictive controller is investigated in the numerical simulations, and the centralized fast model predictive controller is adopted for better comparison. The results demonstrate that the distributed adaptive model predictive controller can effectively suppress vibration of the large space structure during on-orbit assembly, with good adaptability, robustness, and computation efficiency.