The rating of perceived exertion (RPE) and surface electromyography (sEMG) describe exercise intensity subjectively and objectively, while there has been a lack of research on the relationship between them during dynamic contractions to predict exercise intensity, comprehensively. The purpose of this study was to establish a model of the relationship between sEMG and RPE during dynamic exercises. Therefore, 20 healthy male subjects were organized to perform an incremental load test on a cycle ergometer, and the subjects’ RPEs (Borg Scale 6–20) were collected every minute. Additionally, the sEMGs of the subjects’ eight lower limb muscles were collected. The sEMG features based on time domain, frequency domain and time–frequency domain methods were extracted, and the relationship model was established using Gaussian process regression (GPR). The results show that the sEMG and RPE of the selected lower limb muscles are significantly correlated (p < 0.05) but that they have different monotonic correlation degrees. The model that was established with all three domain features displayed optimal performance and when the RPE was 13, the prediction error was the smallest. The study is significant for lower limb muscle training strategy and quantification of training intensity from both subjective and objective aspects, and lays a foundation for sEMG further applications in rehabilitation medicine and sports training.