The popularization of mobile devices connected to the network promotes the rise and development of the emerging mobile Internet of Things (MIoT). Crowdsensing is a promising mode to perceive data in MIoT, where the collection of sensing data is outsourced to the public crowd carrying mobile devices. However, this crowdsensing mode inevitably makes privacy compromised, due to the workers' sensitive information in the sensing data. As such, how to incentivize workers' participation with privacy preservation becomes a challenge. To tackle this problem, in this article, we propose an auction-based privacy-preserving incentive scheme (APIS) for sensing task allocation in MIoT. Specifically, integrating the idea of software-defined network (SDN), we first present a cloud and edge cooperation-based crowdsensing framework, where the cloud is designed as the controller to collect sensing results from the distributed edge nodes and each edge node outsources sensing tasks to participating workers. To motivate workers' participation, we devise a differential privacy-based auction mechanism, whereby each worker can utilize her privacy budget to control how much privacy can be leaked and decide the sensing precision by the sensing time. Moreover, to maximize the utility of the sensing platform, we design a greed-based algorithm to select the winning workers and determine payments to winners. Finally, we conduct extensive simulations to verify the effectiveness of APIS and demonstrate its superiority.