Musculoskeletal robot with high precision and robustness is a promising direction for the next generation of robots. However, motion learning and rapid generalization of complex musculoskeletal systems are still challenging. Therefore, inspired by the movement preparation mechanism of the motor cortex, this article proposes a motion learning framework based on the recurrent neural network (RNN) modulated by initial states. First, two RNNs are introduced as a preparation network and an execution network to generate initial states of the execution network and time-varying motor commands of movement, respectively. The preparation network is trained by a reward-modulated learning rule, and the execution network is fixed. With the modulation of initial states, initial states can be explicitly expressed as knowledge of movements. By dividing the preparation and execution of movements into two RNNs, the motion learning is accelerated to converge under the application of the node-perturbation method. Second, with the utilization of learned initial states, a rapid generalization method for new movement targets is proposed. Initial states of unlearned movements can be computed by searching for low-dimensional ones in latent space constructed by learned initial states and then transforming them into the whole neural space. The proposed framework is verified in simulation with a musculoskeletal model. The results indicate that the proposed motion learning framework can realize goal-oriented movements of the musculoskeletal system with high precision and significantly improve the generalization efficiency for new movements.