The effector trajectory control for the free-floating space robot(FFSR) with uncertain inertial parameters is one of hotpot about FFSR's control. Focusing on this problem, an optimal adaptive tracking control method is proposed. According to the discrete state dependent riccati equation(DSDRE), a two-stage DSDRE optimal controller is designed. By using the controller output and solving a nonlinear optimization problem, inertial parameter identification is solved. By using the result of inertial parameter identification, parameters of the two-stage DSDRE controller are adjusted in order to obtain the optimal adaptive tracking control method. Finally, simulations are carried out with the two-link planar FFSR model, which demonstrates the effectiveness of the propored method.