Coordinated human movement depends on the integration of multisensory inputs, sensorimotor transformation, and motor execution, as well as sensory feedback resulting from body-environment interaction. Building dynamic models of the sensory-musculoskeletal system is essential for understanding movement control and investigating human behaviours. Here, we report a human sensory-musculoskeletal model, termed SMS-Human, that integrates precise anatomical representations of bones, joints, and muscle-tendon units with multimodal sensory inputs involving visual, vestibular, proprioceptive, and tactile components. A stage-wise hierarchical deep reinforcement learning framework was developed to address the inherent challenges of high-dimensional control in musculoskeletal systems with integrated multisensory information. Using this framework, we demonstrated the simulation of three representative movement tasks, including bipedal locomotion, vision-guided object manipulation, and human-machine interaction during bicycling. Our results showed a close resemblance between natural and simulated human motor behaviours. The simulation also revealed musculoskeletal dynamics that could not be directly measured. This work sheds deeper insights into the sensorimotor dynamics of human movements, facilitates quantitative understanding of human behaviours in interactive contexts, and informs the design of systems with embodied intelligence.