The product categories are vital for the e-commerce platforms due to the core applications on automatic product category assignment, personalized product recommendations, etc. Two key aspects of product classification are multi-modal information and fine-grained understanding. However, recent datasets could hardly support both sides. To address this issue, in this paper, we construct a large-scale Multi-modal E-commerce Products classification dataset MEP-3M, which consists of over 3 million products and 599 fine-grained product categories. Each product is represented with an image-text pair and annotated with hierarchical labels. To our best knowledge, MEP-3M is the first e-commerce products dataset paying attention to the multi-modal and fine-grained aspects concurrently, and its scale achieves the largest in existing E-commerce datasets. We also present the performances of the several methods on this dataset as the baselines, where the best accuracy achieves 90.70%. This dataset is now available at https: //github.com/ChenDelong1999/MEP-3M.