Aimed at the existing problems, such as the improving requirements on privacy, and the low quality of collected data in mobile crowd sensing, one online Quality-based Privacy-preserving Task Allocation (QPTA) mechanism is considered in this paper. First, a travel budget-related polynomial is designed to measure the influence of candidate tasks on the whole task quality, and an online task quality-based allocation model is designed to maximize the total task quality when both the budget and time constraints can be satisfied simultaneously. Second, when the perceived data of task participants and requesters are encrypted values, with the introduction of typical Paillier homomorphic encryption technology, the division, the square root, and the Euclidean distance calculations of the encrypted values are then designed. In this way, the encrypt calculations of the task allocation algorithm are solved, and the data privacy of the task allocation system is thus preserved. Finally, the bilateral privacy analysis of the proposed method is illustrated, and some simulations are carried out to show the effectiveness of the proposed method. Simulation results show that the proposed method can allocate tasks effectively while guaranteeing the privacy of both the participants and requesters. It outperforms the most related methods in terms of average perception quality.