Space robots can assist astronauts in accomplishing a variety of space missions in high-risk environments. As spacecraft become increasingly lightweight, large-scale, and integrated, space robots are a type of large-scale robots with flexible links and flexible joints. However, the flexibility of the components complicates robot modeling and controller design. Therefore, to address the issue of stable trajectory tracking for multi-flexible space robots, a dynamics model of space robots with multiple flexibilities is established, and a composite controller is designed to enhance control stability. In modeling, comprehensively considering the rigid joints, joint flexibility and link flexibility, the kinematics is consistently described by using the component deformation matrix and recursive method. An accurate dynamics model is established by Lagrange’s equations. In control, using fuzzy neural network sliding mode control, a rigid subsystem controller is designed to suppress the system jitter caused by sudden parameter changes. And it implements the robust tracking of the robot trajectory. Meanwhile, the weighted average fuzzy controller is designed to control the link deformation. The regulation of the flexible joint by the fast feedback controller is implemented using the virtual torque feedback control. Finally, the validity of the dynamics and control models is verified using Matlab and Adams. Compared with previous studies, this study considers multiple flexibility factors more fully. The vibration of multiple flexible components is suppressed during the stable trajectory tracking of the robot.