The automatic recognition technology of muscle fatigue has widespread application in the field of kinesiology and rehabilitation medicine. In this paper, we used surface electromyography (sEMG) to study the recognition of leg muscle fatigue during circuit resistance training. The purpose of this study was to solve the problem that the sEMG signals have a lot of noise interference and the recognition accuracy of the existing muscle fatigue recognition model is not high enough. First, we proposed an improved wavelet threshold function denoising algorithm to denoise the sEMG signal. Then, we build a muscle fatigue state recognition model based on long short-term memory (LSTM), and used the Holdout method to evaluate the performance of the model. Finally, the denoising effect of the improved wavelet threshold function denoising method proposed in this paper was compared with the denoising effect of the traditional wavelet threshold denoising method. We compared the performance of the proposed muscle fatigue recognition model with that of particle swarm optimization support vector machine (PSO-SVM) and convolutional neural network (CNN). The results showed that the new wavelet threshold function had better denoising performance than hard and soft threshold functions. The accuracy of LSTM network model in identifying muscle fatigue was 4.89% and 2.47% higher than that of PSO-SVM and CNN, respectively. The sEMG signal denoising method and muscle fatigue recognition model proposed in this paper have important implications for monitoring muscle fatigue during rehabilitation training and exercise.