With the ubiquitous deployment of the mobile devices with increasingly better communication and computation capabilities, an emerging model called spatial crowdsourcing is proposed to solve the problem of unstructured big data by publishing location-based tasks to participating workers. However, massive spatial data generated by spatial crowdsourcing entails a critical challenge that the system has to guarantee quality control of crowdsourcing. This paper first studies a practical problem of task assignment, namely reliability aware spatial crowdsourcing (RA-SC), which takes the constrained tasks and numerous dynamic workers into consideration. Specifically, the worker confidence is introduced to reflect the completion reliability of the assigned task. Our RA-SC problem is to perform task assignments such that the reliability under budget constraints is maximized. Then, we reveal the typical property of the proposed problem, and design an effective strategy to achieve a high reliability of the task assignment. Besides the theoretical analysis, extensive experimental results also demonstrate that the proposed strategy is stable and effective for spatial crowdsourcing.