Free-floating flexible manipulator system has become a nonholonomic system subject to the constraints of the conservation of angular momentum. The dynamic model of the nonholonomic system is usually the differential algebraic equation which is difficult to solve. So the free-floating system is translated into holonomic system in this research. First, the attitude of carrier was supposed to be controlled by torques. As a result, the system turned to be holonomic because the constraint of the conservation of angular momentum need not be satisfied, and the dynamic equations of the holonomic system were deduced based on Lagrange method. Second, the dynamic equations of free-floating system were obtained by putting the attitude control torques into zero. Finally, the dynamic equations were solved with numerical method. The numerical result is compared with the simulation result in ADAMS and the effective of the model for free-floating flexible manipulator system is verified.