Smart Grid (SG) is defined to provide power grid with more choices of information services. To efficiently implement modern communication techniques into SG, LTE is widely considered to be most competitive candidate. Although LTE performs well in nowadays mobile communication industry, it still needs optimization during the implementing process. A feature that makes SG communication different from mobile communication is that the Smart Meters, which is considered to be the users in SG-LTE network, don't deserve strictly fair service in the network. In this paper, we proposed a priority-based LTE packet scheduler. Simulation result shows that the proposed solution efficiently improved high priority users' performance. Along with some acceptable system performance cost, the proposed scheduler is suitable for SG communication environment.