Smart meter (SM) is a key component of the smart grid, which reports power consumption to a centralized control center at regular intervals. The long term evolution (LTE) network has gained much attention as an attractive communication platform for SM traffic due to its high bandwidth, low latency, and coverage. However, when a large number of SMs simultaneously access the LTE network, it is very likely to result in preamble congestion. This eventually becomes a contributing factor for prolonged delays at the eNode-B, which would eventually degrade the performance of the LTE network. Hence, a random access mechanism is desirable for preamble signatures to occupy resource blocks for SMs. In this paper, we introduce a novel technique that combines contention- and noncontention-based random access methods. Our proposed method does not require a backoff time and regeneration of a new preamble if the first attempt is unsuccessful. Although SMs have fixed periodic communications, under the proposed random access mechanism preamble signatures do not need to be reserved. We analyze the proposed mechanism's efficiency in terms of metrics collision probability and packet delay. The simulation results are validated against the 3GPP standard.