Virtual metrology (VM) is one of the most important enabling technologies in smart manufacturing. Although there is an abundance of literature on VM applications, the context of continuous production has received less attention. Fundamental challenges involved in the application of VM to a continuous process have been overlooked in comparison with intermittent (or batch) processes. Here, we described a real-world VM system for the manufacturing of spandex fiber, focusing on how practical challenges associated with a continuous process, including time synchronization, recirculation process, and autocorrelated features, can be addressed using data analytics. A model refresh strategy is discussed for the deployed VM system to ensure continuous usability and high-quality predictions. The virtual-physical connection established by the VM system creates a virtuous cycle in which constantly updated data render the system realistic, and valuable insights generated by the system can be applied to the physical production environment.