Joint trajectory tracking control and flexible vibration suppression techniques for a Free-Floating Flexible Space Robot (FFFSR) were discussed under parameter uncertainty and limited torque. A composite controller containing a slow control subsystem for joint trajectory tracking and a fast control subsystem for flexible vibration description were proposed using singular perturbation method. A model-free Fuzzy Radial Basis Function Neural Network (FRBFNN) adaptive tracking control strategy was applied in the slow subsystem. FRBFNN was adopted to support the estimation of velocity signals performed by the observer, the approximation of the unknown nonlinear functions of the observer as well as the controller. The fast subsystem adopted an Extended State Observer (ESO) to estimate coordinate derivatives of flexible modal and uncertain disturbance, which could hardly be measured, and used Linear Quadratic Regulator (LQR) method to suppress the flexible vibration. Numerical simulation results show that the composite controller can achieve stable joint trajectory tracking in 2.5 s, and the flexible vibration amplitude is restricted in ±1×10 ^-3 m, when the control torque is limited within ±20 N·m and ±10 N·m.