Location based services have experienced an explosive growth and evolved from utilizing a single location to the whole trajectory. Due to the hardware and energy constraints, there are usually many missing data within a trajectory. In order to accurately recover the complete trajectory, crowdsensing provides a promising method. This method resorts to the correlation among multiple users' trajectories and the advanced compressive sensing technique, which significantly outperforms conventional interpolation methods on accuracy. However, as trajectories exposes users' daily activities, the privacy issue is a major concern in crowdsensing. While existing solutions independently tackle the accurate trajectory recovery and privacy issues, yet no single design is able to address these two challenges simultaneously. Therefore in this paper, we propose a novel Privacy Preserving Compressive Sensing (PPCS) scheme, which encrypts a trajectory with several other trajectories while maintaining the homomorphic obfuscation property for compressive sensing. Under PPCS, adversaries can only capture the encrypted data, so the user privacy is preserved. Furthermore, the homomorphic obfuscation property guarantees that the recovery accuracy of PPCS is comparable to the state-of-the-art compressive sensing design. Based on two publicly available traces with numerous users and long durations, we conduct extensive simulations to evaluate PPCS. The results demonstrate that PPCS achieves a high accuracy of <;53 m and a large distortion between the encrypted and the original trajectories (a commonly adopted metric of privacy strength) of >9,000 m even when up to 50% original data are missing.