In mobile crowdsensing (MCS), providing appropriate rewards is a common and efficient way to motivate participants to participate in sensing tasks. However, the privacy of task participants is not protected well in most quality-aware incentive schemes. Moreover, these schemes are designed for general MCS application scenarios where data are collected by internal sensors embedded in participants’ smartphones, and not suitable for scenarios where additional sensors (ASs) except internal sensors are to collect data (e.g., household medical devices). In scenarios with ASs, malicious participants can fabricate sensing data instead of collecting data from ASs, i.e., the source reliability of sensing data cannot be ensured. To address these issues, we propose P2SIM, a privacy-preserving and the source-reliable incentive mechanism scheme for MCS with ASs. We combine redactable signature with private hash function to achieve the source reliability verification of sensing data without revealing the privacy of participants. Moreover, rewards are divided into two parts: 1) fixed rewards and 2) floating rewards, to enhance the flexibility of rewards distribution. Both formal theoretical analysis and extensive experimental evaluations on a real data set show that the proposed P2SIM is secure and efficient.