Smart Grid (SG) is considered as an intelligent electricity delivery system due to its advantage of bi-directional mode of data and information flow. This improves the reliability, efficiency and self-controllability on the SG system. One of the important components in SG is the Smart Meter (SM). Its key function is to report power consumption to a centralized control center at regular intervals. The LTE is an attractive platform for SG communications due to its high bandwidth and low latency over a large coverage area. However, LTE was not designed for SM communications that need to access the center in periodic time intervals. This leads to a preamble collision issue, which results in packet loss, delay, and re-establishment attempts. Higher the value of these parameters, lower is the performance of the network. In this paper, we propose a combination of contention and non-contention based random access procedures for SMs to establish connections and transfer of packets using Tracking Area Update. The simulation results show the efficiency of the system in terms of reduced latency. The performance of the system is also compared with the LTE standard.