Wave-induced ship heave and roll motions pose great challenges for the design of control systems of dual ship-mounted cranes (DSCs) along with complicated nonlinearities and physical constraints. Aiming at the above issues, this paper establishes the dynamic model of DSCs subject to ship roll and heave motions and proposes a nonlinear coordinated stabilizing controller which could achieve precise positioning and swing-elimination. First, the DSCs dynamic model considering ship roll and heave motions is built by utilizing the Lagrange method. On the basis of the dynamic model, the system energy function consisting of the kinetic and potential energy is introduced. With the first-order derivation of the energy function, explicit expressions of ship-to-ship interaction forces caused by ship motions are derived. These forces are then incorporated into the controller to mitigate the effects between the two ships, thereby achieving coordinated control of the two cranes during payload transportation. Lyapunov techniques are used to rigorously prove the stability of the control system. Finally, numerous simulations verify the effectiveness of the proposed controller.