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A profound understanding of inter-agent relationships and motion behaviors is important to achieve high-quality planning when navigating in complex scenarios, especially at urban traffic intersections. We present a trajectory prediction approach with respect to traffic lights, D2-TPred, which uses a spatial dynamic interaction graph (SDG) and a behavior dependency graph (BDG) to handle the problem of discontinuous dependency in the spatial-temporal space. Specifically, the SDG is used to capture spatial interactions by reconstructing sub-graphs for different agents with dynamic and changeable characteristics during each frame. The BDG is used to infer motion tendency by modeling the implicit dependency of the current state on priors behaviors, especially the discontinuous motions corresponding to acceleration, deceleration, or turning direction. Moreover, we present a new dataset for vehicle trajectory prediction under traffic lights called VTP-TL. Our experimental results show that our model achieves more than {20.45% and 20.78% }improvement in terms of ADE and FDE, respectively, on VTP-TL as compared to other trajectory prediction algorithms. The dataset and code are available at: https://github.com/VTP-TL/D2-TPred.