In order to improve the joint flexibility of the upper limb exoskeleton robot, an upper limb flexible exoskeleton robot with modular series elastic actuators and Bowden cable is proposed. To reduce the nonlinear friction, unknown external disturbance and model uncertainty caused by Bowden cable, an adaptive composite controller based on radial basis function (RBF) neural network is proposed. The disturbance observer and RBF neural network adaptive controller are used to estimate and compensate the disturbances, and the sliding mode controller is used to implement the tracking control of the upper limb flexible exoskeleton robot. In addition, the stability of the controller is proved by Lyapunov theory. The simulation results show that the proposed controller has better disturbance compensation capability, higher tracking control accuracy and robustness compared with the conventioal proportional integral differential (PID) controller and sliding mode controller, and can realize the precise tracking control of the upper limb flexible exoskeleton robot.