Against the background of globalization, the circulation range of traditional Chinese medicinal materials is constantly expanding, and the phenomena of mixed origins and counterfeiting are becoming increasingly serious. Tracing the origin of traditional Chinese medicinal materials is of great significance for ensuring their quality, safety, and effectiveness. Laser-induced breakdown spectroscopy (LIBS), as a rapid and non-destructive element analysis technique, can be used for the origin tracing of traditional Chinese medicinal materials. Deep learning can not only handle non-linear relationships but also automatically extract features from high-dimensional data. In this paper, LIBS is combined with deep learning, and a Double-Multi Convolutional Neural Network LIBS Analysis System (DMC-LIBSAS) is proposed for the origin tracing of the traditional Chinese medicinal material Angelica dahurica. The system consists of a LIBS signal generation module, a spectral preprocessing module, and an algorithm analysis module—Double-Multi Convolutional Neural Network (DMCNN)—achieving a direct mapping from input data to output results. And the ability of DMCNN to extract characteristic peaks is demonstrated by the 1D Gradient-weighted Class Activation Mapping (1D-Grad-CAM) method. The tracing accuracy of DMC-LIBSAS for Angelica dahurica reaches 95.25%. To further verify the effectiveness of the system, it is compared with six classic methods including LeNet, AlexNet, Resnet18, K-nearest neighbors (KNN), Random Forest (RF), and Decision Tree (DT) (with accuracies of 68%, 75%, 72.5%, 79.7%, 86.7%, and 75.5%, respectively), and the tracing effects are all much lower than that of DMC-LIBSAS. The results show that DMC-LIBSAS can effectively and accurately trace the origin of Angelica dahurica, providing a new technical support for the quality supervision of traditional Chinese medicinal materials.