Industrial Internet of Things (IIoT), as an important industrial branch of the Internet of Things (IoT), has an essential purpose to improve intelligent industrial production. For this purpose, IIoT big data should be efficiently processed to mine valuable information. In handing the IIoT big data, cloud–edge computing is getting more attention to reduce the interaction latency to meet the real-time requirement, especially in the field of prognostic and health management (PHM). It is expected that artificial intelligence (AI) technologies will significantly change the manner of processing IIoT big data. Therefore, new methods about PHM, combining cloud–edge computing with AI technologies, are required to process the IIoT big data for intelligent industrial manufacturing. As an essential element of PHM, predicting the remaining useful life (RUL) of industrial equipment plays an increasingly crucial role, especially for industrial intelligence. However, traditional methods pay much attention on prediction accuracy and neglect the influence of computing time. In this article, by combining cloud–edge computing with AI technology, a new data-driven method, namely, cloud–edge-based lightweight temporal convolutional networks (LTCNs), for RUL prediction is proposed. First, to meet the real-time requirement, a cloud–edge computing and AI-based framework for RUL prediction is presented. Second, a new model structure named LTCN is proposed and applied in the framework. Real-time prediction results will be obtained in the edge plane and higher accuracy prediction results will be obtained through historical information in the cloud plane. Third, an incremental learning approach based on updating partial parameters of LTCN is discussed to improve the accuracy of prediction models with newly collected data. Experiments show that our method can improve the prediction accuracy and reduce the computational time of RUL.