Mobile crowdsensing (MCS) has rapidly emerged as a popular paradigm for sensory data collection and benefited various location-based services and applications like road monitoring, smart transportation, and environmental monitoring. In practice, there often exist data-missing regions in the target sensing area, due to factors like limited budget, large area size, and scarcity of participants. This poses a demand for data recovery, which is commonly done based on the compressive sensing (CS) technique. However, CS-based data recovery requires access to sensory data tagged with locations, raising critical concerns on participants’ location privacy. While a plethora of location privacy techniques exist, most of them breach the data correlation inherently required by CS-based data recovery. Meanwhile, existing works mostly focus on protecting locations and overlook sensory data which may also indirectly lead to location leakages. In this paper, we propose SecDR, a new system design supporting secure, efficient, and accurate data recovery for location-based MCS applications. SecDR protects both locations and sensory data, and is built from a delicate synergy of CS-based data recovery and lightweight cryptography techniques. Extensive evaluations demonstrate that SecDR achieves promising performance and, even with stronger security guarantees, outperforms the state-of-the-art, with accuracy close to the plaintext domain.