The increasing use of GPS-enabled devices has generated a large amount of trajectory data. These data offer us vital insights to understand the movements of individuals and populations, benefiting a broad range of applications from transportation planning to epidemic modeling. However, improper release of trajectory data is increasing concerns on individual privacy. Previous attempts either lack strong privacy guarantees, or fail to preserve sufficient basic characteristics of the original data. In this paper, we propose DPTraj-PM, a method to synthesize trajectory dataset under the differential privacy (DP) framework while ensures high data utility. Based on the assumption that an individual's trajectory could be mainly determined by the initial trajectory segment (which depicts the starting point and the initial direction) and the next location point, DPTraj-PM discretizes the raw trajectories into neighboring cells, and models them by combining a prefix tree structure and an m-order Markov process. After adding noise to the model under differential privacy, DPTraj-PM generates a synthetic dataset from the noisy model to enable a wider spectrum of data mining and modeling tasks. The output traces crafted by DPTraj-PM not only preserves the patterns and variability in individuals' mobility behaviors, but also protects individual privacy. Experiments on two real-world datasets demonstrate that DPTraj-PM substantially outperforms the state-of-the-art techniques in terms of data utility. Our code is available at https://github.com/wnn5/DP-PrefixTreeMarkov.