Dynamic Movement Primitives (DMPs) framework is a powerful approach to imitate motor skills, which has outstanding characteristics, such as convergence to the goal position and good imitation performance. Considering complex motion scenes of manipulators, such as changing the goal position or adding obstacles, the original DMPs framework is not sufficient for the requirements. In this paper, we propose a learning control-based hierarchical control strategy to adapt to new goal positions and avoid obstacles: the high-level learning scheme is targeted at imitating the motor skill and generating the optimization trajectory for obstacle avoidance; the lower-level control scheme focuses on the safety and stability of the robot's movement with unknown disturbances. Firstly, the enhanced DMPs framework is presented to imitate the trajectory from human demonstrations, where the novel DMPs can adapt to new goal position with the changing goal, and avoid single or multiple obstacles. Then, the fuzzy adaptive control method is employed to control redundant manipulators, where the fuzzy logic system (FLS) is incorporated to approximate an unknown nonlinear function term of the unknown disturbance. Finally, the effectiveness of the proposed learning-control strategy is demonstrated with simulation results. The results show that the developed hierarchical strategy has good performance for new goal adaptation and obstacle avoidance.