Incentive mechanism design and quality control are two key challenges in data crowdsourcing, because of the need for recruitment of crowd users and their limited capabilities. Without considering users’ social influences, existing mechanisms often result in low efficiency in terms of the platform’s cost. In this paper, we exploit social influences among users as incentives to motivate users’ participation, in order to reduce the cost of recruiting users. Based on social influences, we design incentive mechanisms with the goal of achieving high quality of crowdsourced data and low cost of incentivizing users’ participation. Specifically, we consider three scenarios. In the full information scenario, we design task assignment and user recruitment mechanisms to optimize the data quality while reducing the incentive cost. In the partial information scenario, users’ qualities and costs are unknown. We exploit the correlation between tasks to overcome the information asymmetry, for both cases of opportunistic crowdsourcing and participatory crowdsourcing. Further, in the dynamic social influence scenario, we investigate the dynamics of users’ social influences and design extra rewards for users to make full use of the social influence and achieve maximum cost saving. We evaluate the incentive mechanisms using numerical results, which demonstrate their effectiveness.