Data anonymisation is of increasing importance for allowing sharing individual data among various data requesters for a variety of social network data analysis and mining applications. Most existing works of data anonymisation target at the optimization of the anonymisation metrics to balance the data utility and privacy, whereas they ignore the effects of a requester’s trust level and application purposes during the data anonymisation. Our aim of this paper is to propose a much finer level anonymisation scheme with regard to the data requester’s trust and specific application purpose. We firstly prioritize the attributes for anonymisation based on their importance to application purposes. Secondly, we build the projection between the trust value and the degree of data anonymiztion, which intends to determine to what extent the data should be anonymized. The decomposition algorithm is developed to find the desired anonymous solution, which ensures the uniqueness and correctness. Finally, we conduct extensive experiments on two real-world data sets and the results show the benefits of our approach for both data requesters and providers.