Time-series prediction plays a crucial role in the Industrial Internet of Things (IIoT) to enable intelligent process control, analysis, and management, such as complex equipment maintenance, product quality management, and dynamic process monitoring. Traditional methods face challenges in obtaining latent insights due to the growing complexity of IIoT. Recently, the latest development of deep learning provides innovative solutions for IIoT time-series prediction. In this survey, we analyze the existing deep learning-based time-series prediction methods and present the main challenges of time-series prediction in IIoT. Furthermore, we propose a framework of state-of-the-art solutions to overcome the challenges of time-series prediction in IIoT and summarize its application in practical scenarios, such as predictive maintenance, product quality prediction, and supply chain management. Finally, we conclude with comments on possible future directions for the development of time-series prediction to enable extensible knowledge mining for complex tasks in IIoT.