Since poor man–machine interaction and insufficient coupling occur in the processes of angle prediction and rehabilitation training based purely on the surface electromyography (sEMG) signal, a model for predicting the angles of upper limb joints was presented and validated by experiments. The sEMG and posture capture features were combined to build a hybrid vector, and the intentions of upper limb movements were characterized. The original signals were pre-treated with debiasing, filtering, and noise reduction, and then they were integrated to obtain signal characteristics. Then, feature values in the time domain, frequency domain, time-frequency domain, and entropy were extracted from the treated signals. The snake optimizer least squares support vector machine (SO-LSSVM) was modeled to predict the angles of upper limb joints to improve the poor precision and slow velocity of existing models in the movement control field. Experimental results showed that the prediction model performed well in predicting the motion trails of human upper limb joints from the sEMG signal and attitude information. It effectively reduced both skewing and error in prediction. Hence, it holds great promise for improving the man–machine coupling precision and velocity. Compared to the conventional LSSVM model, the proposed SO-LSSVM model reduced the training time, execution time, and root mean square error of evaluation parameters by 65%, 11%, and 76%, respectively. In summary, the proposed SO-LSSVM model satisfied the real-time requirement for rehabilitation robots and showed high accuracy and robustness.