Accurate tracking of maneuvering targets remains one of the fundamental challenges in radar and intelligent surveillance systems, due to the nonlinear and time-varying nature of target motion models. This paper presents a hybrid deep learning-based framework for maneuvering target tracking, in which an Interacting Multiple Model (IMM) estimator is integrated with a Mixture of Experts (MoE) architecture built upon a Transformer network. The proposed approach aims to adaptively learn both the transition probabilities among motion models and the underlying target dynamics from observed data, thereby overcoming the inherent limitations of conventional filters such as IMM-EKF and IMM-UKF. In this structure, the Transformer network captures long-term temporal dependencies in target trajectories, while the MoE module dynamically activates specialized subnetworks corresponding to different motion patterns, including constant velocity (CV) and coordinated turn (CT) models. Simulation results under nonlinear and noisy conditions demonstrate that the proposed MoE–Transformer–IMM algorithm achieves superior performance in terms of Root Mean Square Error (RMSE) compared to classical IMM-based methods. Furthermore, it exhibits higher stability and accuracy under abrupt maneuvers and sensor noise, achieving up to 89.75% performance improvement over benchmark algorithms, making it a promising candidate for real-world radar tracking applications.