Participating in mobile services by synthesizing trajectories with consistent lifestyle and meaningful mobility as actual traces are the most popular way to protect location privacy. However, recent trajectory synthesizing techniques are still threatened by the information that the attacker inevitably obtains, such as the locations of the accepted tasks in the crowdsourcing application. With this information and the spatiotemporal correlation hidden in the user's mobility, the attacker can infer the user's actual location and even future behaviors. It remains open to defend against such inferential attacks in the continual crowdsourcing scenarios. In this paper, we propose a mobility-aware differentially private solution, ConCrowd-DP, for achieving the privacy-preserving continual crowdsourcing application. Specifically, before starting the application, we first construct a spatiotemporal mobile model, STMarkov, to model the spatiotemporal correlation in users' mobility. Then, a perturbed location is generated for the user to participate in the crowdsourcing application, according to STMarkov and K-norm DP. Finally, we eliminate the privacy threat brought by the accepted task based on K-norm DP and Bayesian posterior theorem. With ConCrowd-DP in place, a mobility-aware differentially private trace is generated for the user to participate in the application continually. Extensive experiments with real-world datasets demonstrate that ConCrowd-DP guarantees the usability of the synthesized trajectory effectively, while providing the DP protection for defending against the inferential attacks which stem from the multiple accepted tasks.