In order to improve the tracking performances of a target with multiple motion models and a high level of maneuvering, this paper proposes a modified maneuver target tracking algorithm (i.e. MIMM-CSRF) based on the traditional Interacting Multiple Model Centralized Shifted Rayleigh Filter (IMM-CSRF) algorithm. A two-stage acceleration correction method based on median filtering and the "current" statistical model is adaptively applied to track a higher-level or lowerlevel maneuvering target. Monte Carlo simulation results show that our algorithm has much better accuracy, stability and generalization of target tracking than the Centralized Extended Kalman Filter(IMM-CEKF), the Unscented Kalman Filter (IMM-CUKF) and IMM-CSRF.