In this paper, we study the problem of mobile data offloading for a network that contains multiple mobile network operators (MNOs), multiple WiFi or femtocell access points (APs) and multiple mobile users (MUs). MNOs offload their subscribed MUs` data traffic by leasing the unused Internet connection bandwidth of third party APs. We propose a combinatorial auction-based two-stage matching mechanism comprised of MU-AP matching and AP-MNO matching. The MU-AP matching is designed to match the MUs to APs in order to maximize the total offloading data traffic and achieve better MU satisfaction. Conversely, for AP-MNO matching, MNOs compete for APs` service using the Nash bargaining solution (NBS) and the Vickrey auction theories and, in turn, APs will receive monetary compensation. We demonstrated that the proposed mechanism converges to a distributed stable matching result. Numerical results demonstrate that the proposed algorithm well capture the tradeoff among the total data traffic, social welfare and the QoS of MUs compared to other schemes. Moreover, the proposed mechanism can considerably offload the total data traffic and improve the network social welfare with less computation complexity and communication overhead.