Traditional model-based distributed maneuvering target tracking methods often require prior knowledge of both sensor and target models, which can lead to significant degradation in tracking accuracy when faced with model mismatches. To address this problem, this paper presents a novel model-based deep learning distributed maneuvering target tracking method over a homogeneous sensor network. Specifically, two deep neural networks are designed to obtain noise-eliminated measurements and timely estimate the motion model of the target. Further, hybrid consensus on measurements and consensus on information method is utilized to fuse local filtering results. Finally, the simulation experiment demonstrates the effectiveness of the proposed method.