The glass relics are precious material evidence of the early trade and cultural exchange between the East and the West. To explore the cultural differences and trade development between early China and foreign countries, it is extremely important to classify glass cultural relics. Despite their similar appearances, Chinese glass contains more lead, while foreign glass contains more potassium. In view of this, this paper proposes a joint Daen-LR, ARIMA-LSTM, and MLR machine learning algorithm (JMLA) for the analysis and identification of the chemical composition of ancient glass. We separate the sampling points of ancient glass into two systems: lead-barium glass and high-potassium glass. Firstly, an improved logistic regression model based on a double adaptive elastic network (Daen-LR) is used to select variables with both Oracle and adaptive classification characteristics. Secondly, the ARIMA-LSTM model was used to establish the correlation curve of chemical composition before and after weathering and to predict the change in chemical composition with weathering. Thirdly, combining the data processed by the above two methods, a multiple linear regression model (MLR) is used to classify unknown glass products. It was shown that the sample obtained by this processing method has a very good fit. In comparison with other similar types of models like Decision Trees (DT), Random Forests (RF), Support Vector Machines (SVM), and Random Forests based on classification and regression trees (CART-RF), the classification accuracy of JMLA is 97.9% on the train set. The accuracy rate on the test set reached 97.6%. The results of the research demonstrate that JMLA can improve the accuracy of the glass type classification problem, greatly enhance the research efficiency of archaeological staff, and gain a more reliable result.