As a wave of the rapidly approaching future, vehicles are becoming increasingly “smarter” via equipping with abundant resources for data sensing, processing, and transmitting. To fully make use of these resources, mobile crowdsourcing applications have attracted particular interests from academia and industry, and they are extensively integrated with fog computing for obtaining low latency and location sensitivity. In this paper, we consider a fog-based task allocation service for mobile crowdsourcing tasks with multiple locations, where a task is allocated to the worker whose future trajectory has the smallest Hausdorff semi-distance to the task locations. However, as fog nodes are not fully trusted, there may exist privacy concerns related to the workers and the task owners. To the best of our knowledge, although Hausdorff semi-distance has been applied in various applications, none of the existing works can support privacy-preserving Hausdorff semi-distance evaluation or nearest neighbor queries. Aiming at this issue, we design a privacy-preserving fog-based multi-location task allocation scheme. Specifically, based on a symmetric homomorphic encryption technique, we build two privacy-preserving protocols for i) computing min/max value from an array and ii) retrieving the key linked to the minimum value from an array of key-value pairs. Then, the proposed scheme is built upon these two protocols. After that, we conduct rigid security analysis and extensive experiments to demonstrate the security and efficiency of our proposed scheme, respectively. The results indicate that our proposed scheme is not only privacy-preserving, but also efficient in terms of both computation and communication costs.