We study a single task allocation problem where each worker connects to some other workers to form a network and the task requester only connects to some of the workers. The goal is to design an allocation mechanism such that each worker is incentivized to invite her neighbours to join the allocation, although they are competing for the task. Moreover, the performance of each worker is uncertain, which is modelled as the quality level of her task execution. The literature has proposed solutions to tackle the uncertainty problem by paying them after verifying their execution. Here, we extend the problem to the network setting. We propose a new mechanism that guarantees that inviting more workers and reporting/performing according to her true ability is a dominant strategy for each worker. We believe that the new solution can be widely applied in the digital economy powered by social connections such as crowdsourcing.