With the rapid development of wireless communication and localization technologies, the easier collection of trajectory data can bring potential data-driven value. Recently, there has been an increasing interest in how to publish trajectory dataset without revealing personal information. However, since the large-scale and real-world sequential trajectory dataset presents a heterogeneous regional distribution, the existing study ignores the relationship between privacy budget allocation and spatial characteristics, resulting in unreasonable continuity and mapping distortion, and thus lowering the utility of the synthetic dataset. To address this problem, we propose a probability distribution model named Adaptive grid-based Weighted Differential Privacy (AWDP). First, trajectories are adaptively discretized into the multi-resolution grid structures to make trajectories more uniformly distributed and less disturbed by the noise. Second, we allocate different weighted budgets for different grids according to density-based regional characteristics. Third, a spatio-temporal continuity maintenance method is designed to solve unrealistic direction- and density-based continuity deviations of synthetic trajectories. An application system is developed for demonstration purposes which is available online at http://qgailab.com/awdp/