Wireless sensor networks are employed in diverse range and are growing area of research and development due to the importance and necessity of applications. Wireless sensor networks depend on batteries with limited power and cannot be recharged or replaced often. Extending the lifetime of wireless sensor networks is a key issue that is being discussed in recent years. The lifetime of the wireless sensor networks can in one way be maximized by proper scheduling of the working of the sensors in such a way that the targets are all covered and the active sensors stay connected to the main server. This paper proposes a genetic algorithm for connected coverage problem that considers the coverage of the targets as well as the connectivity of the sensors with the base station. Genetic algorithms based on the concepts of natural selection and natural evolution can be used to find optimal combinations of sensors in order to extend the lifetime of the network. Genetic algorithm manipulates a population of candidates to provide an optimal solution in each successive generation. The solution obtained by using genetic algorithm ensures that all targets are covered by each sensor cover and connectivity exists between these sensor covers and the base station. Simulation results on various instances confirms that genetic algorithm maximize the lifetime of sensor network and achieves efficient coverage and connectivity.