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Smart grid can be visualized as an intelligent control system over sensors and communication platforms. Recently, wireless multimedia sensor networks (WMSNs) have shown its advantages for smart grid by providing rich surveillance information for grid failure detection and recovery, energy source monitoring, asset management, security, etc. On the other hand, cognitive radio (CR) networks have been identified as a key wireless technology to reduce the communication interferences and improve the bandwidth efficiency for smart grid communication. There is an essential need to use the CR communication platform to support large-size and time-sensitive multimedia delivery for future smart grid system. In this paper, we consider the heterogeneous characteristics of smart grid traffic including multimedia and propose a priority-based traffic scheduling approach for CR communication infrastructure based smart grid system according to the various traffic types of smart grid such as control commands, multimedia sensing data and meter readings. Specifically, we develop CR channel allocation and traffic scheduling schemes taking into consideration of channel switch and spectrum sensing errors, and solve a system utility optimization problem for smart grid communication system. Our solutions are demonstrated through both analyzes and simulations. This research opens a new vista of future smart grid communications.