Recently, foundation models (such as ChatGPT) have emerged with powerful learning, understanding, and generalization abilities, showcasing tremendous potential to revolutionarily promote modern industry. Despite significant advancements in various fields, existing general foundation models face challenges in industry when dealing with the data of specialized modalities, the tasks of varying-scenario with multiple processes, and the requirements of trustworthy output, which makes industrial foundation model (IFM) a necessity. This article proposes a system architecture of termed IFMsys, including model training, model adaptation, and model application. Specifically, in model training, a base model is constructed by pretraining on multimodal industrial data and fine-tuning with fundamental industrial mechanisms. In model adaptation, the base model is developed into a series of task-oriented and domain-specific IFMs through fine-tuning with representative tasks and domain knowledge. In model application, an industrial agent-centric collaboration system and a comprehensive application framework of IFM are proposed to enhance the industrial product lifecycle applications. In addition, a prototype system of the IFM, namely, MetaIndux, is delivered, with application examples presented in typical industrial tasks. Finally, future research directions and open issues of IFM are prospected. We hope this article will inspire the advancements in the theories, technologies, and applications in this emerging research field of IFM.