Process industries cover a wide set of industries, in which the processes are controlled by a combination of distributed control systems (DCSs) and programmable logic controllers (PLCs). These control systems utilize various measurements such as pressure, flow, and temperature to determine the state of the process and then use field devices such as valves and other actuating devices to manipulate the process. Since there are many different types of field devices and since each device is calibrated to its specific installation, when monitoring devices, it is important to be able to transfer not only the device measurement and diagnostics but also characteristics about the device and the process in which it is installed. The current monitoring architecture, however, creates challenges for continuous monitoring and analysis of diagnostic data. In this paper, we present the design of an Industrial Internet-of-Things (IIoT) system for supporting large-scale and continuous device condition monitoring and analysis in process control systems. The system design seamlessly integrates existing infrastructure [e.g., highway addressable remote transducer (HART) and WirelessHART networks, and DeltaV DCS] and newly developed hardware/software components (e.g., one-way data diode and IoT cellular architecture) together for control network data collection and streaming of the collected device diagnostic parameters to a private cloud to perform streaming data analytics designed for fault identification and prediction. A prototype system has been developed and supported by Emerson Automation Solutions and deployed in the field for design validation and long-term performance evaluation. To the best of our knowledge, this is the first ever publicly reported effort on IoT system design for process automation applications. The design can be readily extended for condition monitoring and analysis of many other industrial facilities and processes.