Crowdsensing is a sensing method which involves participants from general public to collect sensed data from their mobile devices, and also contribute and utilize a common database. To ensure a crowdsensing system to operate properly, there must be certain effective and efficient incentive mechanism to attract users and stimulate them to submit sensing data with high quality. Intuitively, the agreement on the qualities and payments in crowdsensing systems can be best modeled as a contract. However, none of existing incentive mechanisms consider data quality through effective contract design. In this paper, we design two quality-aware contract-based incentive mechanisms for crowdsensing, named QUAC-F and QUAC-I, under full information model and incomplete information model, respectively, which differ in the level of users' information known to the system. Both QUAC-F and QUAC-I are guaranteed to maximize the platform utility while satisfying individual rationality and incentive compatibility. We evaluate the performance of our designed mechanisms based on a real dataset.