Sign languages are developed around the world for hearing-impaired people to communicate with others who understand them. Different grammar and alphabets limit the usage of sign languages between different sign language users. Furthermore, training is required for hearing-intact people to communicate with them. Therefore, in this paper, a real-time motion recognition system based on an electromyography signal is proposed for recognizing actual American Sign Language (ASL) hand motions for helping hearing-impaired people communicate with others and training normal people to understand the sign languages. A bilinear model is applied to deal with the on electromyography (EMG) data for decreasing the individual difference among different people. A long short-term memory neural network is used in this paper as the classifier. Twenty sign language motions in the ASL library are selected for recognition in order to increase the practicability of the system. The results indicate that this system can recognize these twenty motions with high accuracy among twenty participants. Therefore, this system has the potential to be widely applied to help hearing-impaired people for daily communication and normal people to understand the sign languages.