Current years Wireless Sensor networks is a leading area in research due to its number of applications in massive areas .The major concern for Wireless sensor networks is an issue of power of batteries for sensor nodes , several algorithms were transcribed to solve this problem but in so many cases only energy efficiency is considered , coverage problem with energy efficiency is not addressed in most of the cases. To give a better solution for energy efficiency and coverage in this paper modified LEACH protocol is proposed with genetic algorithm, which gives comparatively better results than EBRP protocol