Abstract: Because there are special micro gravity environments in the space and the barycenter of the satellite main body isn’t fixed, the Newton Euler method to calculate the joint torque proposed by Luh’s group and the conventional control strategy for the ground fixed robots can’t be directly applied to free flying space robots（FFSR）. First, the velocity and acceleration for FFSR are analyzed, and the recursive formula for calculating the velocity and acceleration of the links of FFSR are established. Then, based on the Newton Euler dynamics method for the ground fixed robots proposed by Luh et al , a recursive algorithm of joint driving torque for FFSR is developed. Finally, the computer simulation verifies the effectiveness of the proposed joint torque algorithm.