Smart meters are utilized to transmit the consumption information to the metering data management system for observing and management in smart grid advanced metering infrastructure systems. In the meantime, for efficient utilization for spectrum, Device-to-Device (D2D) communications underlaying LTE networks are a promising wireless communication technology for advanced metering infrastructure which supporting a technique for reusing the same radio resources (RRs) of LTE networks. Therefore, we examine the utilization of D2D communication technology for advanced metering infrastructure communications underlaying LTE networks. A novel approach is suggested for provisioning the mandatory communication between serving data concentrator and its set of smart meters using this technology. The suggested approach is dependent on two main stages. The group of permissible cellular user equipment reuse candidates for every smart meter is calculated with taking the quality of service demands for cellular user devices and smart meters into consideration in the first stage. The optimal RR allocation for every smart meter is determined based on maximizing the access rate of smart meters which can be accepted and operated in D2D reuse mode in the second stage. Simulation results prove the efficacy of the suggested approach for efficient advanced metering infrastructure communication underlaying LTE systems with accepting remarkable number of SMs and accomplishing outstanding throughput gain.