The proliferation of mobile smart devices with ever-improving sensing capacities means that Mobile Crowd Sensing (MCS) can economically provide a large-scale and flexible solution. However, existing MCSs face threats to privacy and fairness when recruiting workers due to information sensitivity, uncertainty about worker behavior, and budget constraints. To address the above issues, we propose an Anonymity, Trust, and Fairness in Privacy Protection (ATFPP) service construction framework to cost-effectively improve the quality of data at MCS. The main innovations are as follows: Firstly, on anonymity, in order to protect the privacy of workers, we propose a Privacy-Preserving (PP) framework based on an anonymous three-party platform, which realizes a full-process privacy-preserving scheme for workers. Second, on trust, we design more efficient Truth Discovery (TD) algorithm and adopt multifactor trust assessment method to identify more trustworthy workers. In addition, in terms of fairness, the fair distribution of compensation is realized through reasonable budget and approximate Shapley method. Finally, the proposed ATFPP scheme is theoretically proven to be correct and effective. Simulations based on real-world datasets illustrate that our ATFPP service construction scheme outperforms the state-of-the-art method in terms of both privacy protection and data quality.