Complex behavioral tasks like grasping require precise and accurate motor control. This demands an intricate interplay between proprioceptive processing and motor command generation within the sensorimotor system. While the task-driven modeling approach has proven successful in capturing sensory representations, adapting it to model the sensorimotor system has remained a challenge. Here, we investigate the potential of deep reinforcement learning to capture sensorimotor representations. By training artificial agents to imitate natural grasp movements using imitation learning, we develop stimulus-computable models that effectively capture sensorimotor representation by predicting the neural activity of primates during grasping movements. We show that these models outperform classic encoding models. These results suggest that deep reinforcement learning has the potential to bridge the gap between artificial and biological sensorimotor systems, providing valuable insights into the mechanisms underlying sensorimotor integration and control.