EMG-based continuous wrist joint motion estimation has been identified as a promising technique with huge potential in assistive robots. Conventional data-driven model-free methods tend to establish the relationship between the EMG signal and wrist motion using machine learning or deep learning techniques, but cannot interpret the functional relationship between neuro-commands and relevant joint motion. In this paper, an EMG-driven musculoskeletal model is proposed to estimate continuous wrist joint motion. This model interprets the muscle activation levels from EMG signals. A muscle-tendon model is developed to compute the muscle force during the voluntary flexion/extension movement, and a joint kinematic model is established to estimate the continuous wrist motion. To optimize the subject-specific physiological parameters, a genetic algorithm is designed to minimize the differences of joint motion prediction from the musculoskeletal model and joint motion measurement using motion data during training. Results show that mean root-mean-square-errors are 10.08°, 10.33°, 13.22° and 17.59° for single flexion/extension, continuous cycle and random motion trials, respectively. The mean coefficient of determination is over 0.9 for all the motion trials. The proposed EMG-driven model provides an accurate tracking performance based on user's intention.