The accuracy in maneuvering target tracking using multiple models is resulted in by the suitability of each target motion model to be used. The interacting multiple model (IMM) method and the adaptive IMM (AIMM) method require the predefined sub-models and the predetermined acceleration intervals, respectively, in consideration of the properties of maneuvers in order to construct multiple models. In this paper, to solve these problems, a genetic algorithm(GA) based-IMM method using fuzzy logic is proposed. In the proposed method, the acceleration input is regarded as an additive noise and a sub-model is represented as a set of fuzzy rules to calculate the time-varying variances of the process noises of a new piecewise constant white acceleration model. The proposed method is compared with the AIMM algorithm in simulation.