This work focuses on robust acoustic source localization in sensor networks with limited energy reserve, e.g. Wireless sensor networks (WSN). Real-world data revealed that the acoustic energy gathered at sensors exhibits a heavy-tail, non-Gaussian characteristic and should be fitted into a contaminated Gaussian model. This property causes conventional least square and maximum likelihood based localization methods ineffective. Hence an Energy-efficient robust acoustic source localization protocol (ERASLP) is proposed. With the ERASLP, each sensor receives observations from neighbors then examines its observation by a Local outlier rejection rule (LORR) such that detected outliers are not sent to the fusion center in order to reserve energy and reduce fusion risk. Further analysis show that the communication energy cost of ERASLP is related to the node density and outlier probability. Simulations show that LORR effectively surpasses outliers and that ERASLP has better tradeoff between robustness and energy consumption in most cases.