With the explosive increase of mobile traffic in recent years, cellular networks face enormous challenges in high quality of service (QoS) provisioning for mobile users. Mobile data offloading is a promising way to address this issue, through which a cellular system can reduce its traffic burden by offloading some portion of data to other networks, such as Wi-Fi. However, when the Wi-Fi networks are deployed by different operators, an efficient incentive mechanism is needed to encourage the participation of these networks. However, most of the existing studies on the incentive mechanism design focus on the amount of data offloading from the cellular network, rather than the diverse data patterns and features of different applications. In this paper, we propose a QoS-based incentive mechanism, termed QBIM, to promote the cooperation of multiple offloading networks while achieving high QoS level for mobile users with different applications. Through this mechanism, the cellular network chooses the Wi-Fi access points to offload data traffic of mobile users by jointly considering access point operators' bid vectors and the mobile user utilities of different services. Meanwhile, the corresponding payments are designed as the compensation to the involved Wi-Fi systems. The proposed incentive mechanism can not only achieve the maximum social welfare, but satisfy desirable properties of individual rationality and truthfulness as well. Simulation results show that the proposed mechanism achieves a higher utility with a smaller cost compared to the other counterparts.