<p>This study examines the adaptive boundary control problem of flexible marine riser with internal flow coupling. The dynamic model of the flexible marine riser system with internal flow coupling is derived using the Hamiltonian principle. An analysis of internal flow’s influence on the vibration characteristics of flexible marine risers is conducted. Then, for the uncertain environmental disturbance, the adaptive fuzzy logic system is introduced to dynamically approximate the boundary disturbance, and a robust adaptive fuzzy boundary control is proposed. The uniform boundedness of the closed-loop system is proved based on Lyapunov theory. The well-posedness of the closed-loop system is proved by operator semigroup theory. The proposed control’s effectiveness is validated through comparison with existing control methods.</p>