The time-varying and individual variability of surface electromyographic signals (sEMG) can lead to poorer motor intention detection results from different subjects and longer temporal intervals between training and testing datasets. The consistency of using muscle synergy between the same tasks may be beneficial to improve the detection accuracy over long time ranges. However, the conventional muscle synergy extraction methods, such as non-negative matrix factorization (NMF) and principal component analysis (PCA) have some limitations in the field of motor intention detection, especially in the continuous estimation of upper limb joint angles. In this study, we proposed a reliable multivariate curve-resolved-alternating least squares (MCR-ALS) muscle synergy extraction method combined with long-short term memory neural network (LSTM) to estimate continuous elbow joint motion by using the sEMG datasets from different subjects and different days. The pre-processed sEMG signals were then decomposed into muscle synergies by MCR-ALS, NMF and PCA methods, and the decomposed muscle activation matrices were used as sEMG features. The sEMG features and elbow joint angular signals were input to LSTM to establish a neural network model. Finally, the established neural network models were tested by using sEMG dataset from different subjects and different days, and the detection accuracy was measured by correlation coefficient. The detection accuracy of elbow joint angle was more than 85% by using the proposed method. This result was significantly higher than the detection accuracies obtained by using NMF and PCA methods. The results showed that the proposed method can improve the accuracy of motor intention detection results from different subjects and different acquisition timepoints. This study successfully improves the robustness of sEMG signals in neural network applications using an innovative muscle synergy extraction method. It contributes to the application of human physiological signals in human-machine interaction.