To address the limitation that lower-limb exoskeletons cannot adapt to personalized motion demands, a continuous knee joint angle prediction method based on surface electromyography (sEMG) was proposed and evaluated. The limitation arises from the difficulty of accurately perceiving human movement intention during human-robot interaction rehabilitation tasks. Firstly, the collected sEMG signals were filtered, and features were extracted using a sliding time-window method. Secondly, a prediction model named GAPSO-BP was developed by combining genetic algorithm (GA) and particle swarm optimization (PSO) to optimize a back propagation (BP) neural network. The predicted angles were then compared with the actual angles. Finally, a knee exoskeleton human-robot interaction platform was also built using a mirror-control experimental scheme, and system validation was conducted through motion-tracking and assistance-effectiveness tests. Results show that the prediction accuracy of the GAPSO-BP model increases by 4%, 6%, and 7% compared with BP, radial basis function (RBF), and extreme learning machine (ELM) models. In motion-tracking evaluation, the average coefficient of R-Squared, root mean square error, and normalized root mean square error are 91.61%, 2.029°, and 7.328%. In assistance-effectiveness evaluation, the average assistance efficiency is 37.27%. The proposed GAPSO-BP algorithm improves prediction accuracy and provides a reliable human-robot interaction approach for lower-limb exoskeleton systems.