In today's Industry 4.0 era, information technology has penetrated every industry, making work easier, faster and helping businesses operate more effectively. The ultimate measure of a business's success is customer satisfaction and loyalty. This work aims to enhance customer care by automating the processing of customer feedback through the development of an automatic classification system using deep learning techniques, specifically the Long Short-Term Memory model. The system will automatically classify customer problems, thereby improving service quality and enhancing the company's image. The study used customer feedback data from our company's customer care system, including 41,886 comments from Vietnamese customers. The study proposes to use the LSTM model to process text data and solve the problem of imbalanced data to improve the accuracy and efficiency of the classification system. Test results of the models show that the highest accuracy is about 80%. The study also recommends improving data labeling and testing more advanced natural language processing techniques to achieve better performance in the future.