The study deals with the fleet allocation problem in public electric vehicle (EV) systems with consideration of demand uncertainty. The problem aims to determine the optimal number of EVs deployed at each station and the objective is to minimize the total system cost. We propose a genetic algorithm (GA) with an event-based simulator to solve this problem. To consider demand uncertainty, an event-based simulator is developed and embedded in the GA. This study generates and solves a number of instances based on the historical data obtained from an EV-Sharing system operator in Sun Moon Lake national park in Taiwan. We compare the solutions of the GA with those of an enumeration method. The results show that the GA is able to obtain the optimal solution for more than 70% of the instances. Even when the GA fails to find the optimum, the gaps between optimal solutions and heuristic solutions are less than 0.1%. Moreover, all solutions are found within a reasonable amount of time. The proposed solution approach provides decision support for the fleet allocation in EV-sharing systems.