Recently, mobile social cloud (MSC), formed by mobile users with social ties, has been advocated to allocate tasks of big data applications instead of relying on the conventional cloud systems. However, due to the dynamic topology of networks and social features of users, how to optimally allocate tasks to mobile users based on the trust becomes a new challenge. Therefore, this paper proposes a novel incentive scheme based on the trust of mobile users in the MSC to allocate the tasks of big data. First, a social trust degree is defined according to the social tie among users, the importance of task, and the available resources of networks. With the social trust degree, the task owner can select a group of mobile users as the candidates for task allocation. Second, a reverse auction game model is developed to study the interactions among the task owner and the candidates. With the reverse auction game model, the optimal strategy of task allocation can be obtained with a low cost for the task owner where the selected candidate of mobile users can also obtain the high profit. Finally, simulation experiments are carried out to prove that the proposal can outperform other existing methods with a low delay and a high efficiency to allocate tasks in the MSC.