In the domain of maneuvering target tracking, conventional algorithms frequently utilize multiple predefined mathematical models to approximate target motion. Nonetheless, the intrinsic randomness and unpredictability of maneuvering targets present significant challenges for accurate motion modeling. To address these challenges, this article proposes a novel Transformer-aided multiple model (TAMM) algorithm for maneuvering target tracking. The primary innovation of the TAMM algorithm is the integration of a Transformer-aided recognition module (TARM), which significantly enhances adaptability to the frequent state changes encountered in target tracking. In addition, a dynamic adjustment strategy is implemented to optimize the tracking process, aligning the most suitable motion model and turn rate with each phase, guided by the TARM's output. Extensive simulation results affirm that the proposed algorithm outperforms the traditional UKF algorithm and the interactive multiple model (IMM) algorithm, as well as the DeepMTT algorithm and the TBN algorithm based on deep learning in terms of stability and localization accuracy across diverse scenarios characterized by varying positions, velocities, and turn rates.