The smart grid is a modern electricity grid that uses wireless technologies to control and supervise the substation and the electricity generation and consumption sides. Several wireless technologies can be used for smart grid communication such as Long-Term evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX). However, LTE is the most compatible network for the smart grid because of its reliability and stability. Moreover, LTE provides users with high data rate and low latency. The smart grid performance highly depends on scheduling, because it allocates the Resources Block (RBs) among users taking into consideration the Quality of Service requirements. LTE has not been designated for smart grid communications, leading to unfair bandwidth resources allocation among the smart grid users and the mobile users. This paper proposes a new scheduling scheme that classifies the users into classes based on Packet Loss Ratio (PLR). Then, the bandwidth resources are allocated among classes with different proportion according to PLR for each class. The real-time users in a class are prioritized according to their delay and PLR based on Modified-Largest Weighted Delay First (M-LWDF) algorithm, and non-real-time users are scheduled based on Proportional Fairness algorithm. The performance of the proposed scheme is evaluated in terms of PLR, throughput, delay, and fairness, and compared with Proportional Fairness (PF), Modified-Largest Weighted Delay First (M-LWDF), and Exponential-Rule (EXP-Rule) schemes. The proposed scheme outperforms others in all studied parameters.