High data quality and low sensing cost are two primary goals in large-scale mobile crowdsensing applications. The oversampling and the undersampling are common problems which always result in a high cost or low data quality that can not satisfy the system requirement. To address this problem, taking into account low-rank latent structure, we propose a compressive and adaptive data sampling scheme (CAS) which exploits adaptivity to identify locations which are highly informative for learning the low-dimensional space of the data matrix. In contrast to existing random sampling methods, it involves a three-pass sampling procedure that firstly assigns a fraction of samples to estimate general information, then samples those more informative locations for exact recovery and finally estimates the values of the unsensing locations. Evaluations on synthetic datasets and real datasets for air quality monitoring show the effectiveness of CAS. The experimental results demonstrate that the proposed scheme is able to not only significantly improve the sensing data quality but also reduce the computation complexity comparing with the state-of-the-art matrix completion methods.