With the proliferation of technologies such as wireless sensor networks (WSNs) and the Internet of things (IoT), we are moving towards the era of automation without any human intervention. Sensors are the principal components of the WSNs that bring the idea of IoT into reality. Over the last decade, WSNs are being used in many application fields such as target coverage, battlefield surveillance, home security, health care monitoring, and so on. However, the energy efficiency of the sensor nodes in WSN remains a challenging issue due to the use of a small battery. Moreover, replacing the batteries of the sensor nodes deployed in a hostile environment frequently is not a feasible option.Therefore, intelligent scheduling of the sensor nodes for optimizing its energy-efficient operation and thereby extending the life-time of WSN has received a lot of research attention lately. In particular, this article investigates extending the lifetime of the WSN in the context of target coverage problems. To tackle this problem, we propose a scheduling technique for WSN based on a novel concept within the theory of learning automata (LA) called pursuit LA. Each sensor node in the WSN is equipped with an LA so that it can autonomously select its proper state, that is, either sleep or active, with an aim to cover all targets with the lowest energy cost possible. Our comprehensive experimental testing of the proposed algorithm not only verifies the efficiency of our algorithm, but it also demonstrates its ability to yield a near-optimal solution. The results are promising, given the low computational footprint of the algorithm.