Research in cognitive science reveals that human central nervous system internally simulates dynamic behavior of the motor system using internal models (forward model and inverse model). Being inspired, the question of how a robot develops its internal models for arm motion control is discussed. Considering that human proprioception plays an important role for the development of internal models, we propose to use autoencoder neural networks to establish robot proprioception, and then based on which the robot develops its internal models. All the models are learned in a developmental manner through robot motor babbling like human infants. To evaluate the proprioception-based internal models, we conduct experiments on our PKU-HR6.0 humanoid robots, and the results illustrate the effectiveness of the proposed approach. Additionally, a framework integrating internal models is further proposed for robot arm motion control (reaching, grasping and placing) and its effectiveness is also demonstrated.