In mobile wireless sensor network, coverage and energy conservation are two prime issues. Sensor movement is required to achieve high coverage. But sensor movement is one of the main factors of energy consumption in mobile wireless sensor network. Therefore, coverage and energy conservation are correlated issues and quite difficult to achieve at the same time. In this paper, these conflicting issues are considered, using one of the latest Bio-inspired algorithms, known as Glowworm Swarm Optimization algorithm. Considering the limited energy of sensors, this paper presents an Energy Efficient Multi-Parameter Reverse Glowworm Swarm Optimization (EEMRGSO) algorithm, to move the sensors in an energy efficient manner. Our proposed algorithm reduces redundant coverage area by moving the sensors from densely deployed areas to some predefined grid points. In this proposed algorithm, energy consumption is reduced by decreasing the number of moving sensors as well as the total distance traversed. Simulation results show that, our proposed EEMRGSO algorithm reduces total energy consumption utmost 60% compared to the existing approach based on Glowworm Swarm Optimization algorithm. At the same time, our proposed algorithm reduces the number of overlapped sensors significantly and achieves an effective coverage of 80–89% approximately.