Musculoskeletal robots have structural advantages of flexibility, robustness, and compliance. However, the control of such musculoskeletal robots is challenging. In particular, the efficiency and generalization of motion learning for such robots are still limited. Inspired by motor preparation theories of the motor cortex and motor primitives in neuroscience, a novel neuromuscular control method with high learning efficiency and great generalization is proposed. First, a recurrent neural network (RNN)-based neuromuscular controller is proposed, which autonomously evolves from the initial state of neurons to generate muscle excitations. Second, the motor primitive of initial states in an RNN is proposed and constructed as common knowledge for muscle control. Third, a motion learning method for the modulation of motor primitives is proposed. In the experiments, the proposed method is validated by a redundant musculoskeletal robot and compared with related methods. It demonstrates better performance in terms of learning efficiency, accuracy, and generalization. In addition, the fault tolerance of initial states is analyzed and the robustness to noise is demonstrated.