Pervasive social networking (PSN) supports instant social activities anywhere and at any time with the support of heterogeneous networks. In order to preserve privacy and achieve trustworthy PSN, anonymous authentication on node trust is expected in PSN. However, the literature still lacks serious studies on this issue. In this paper, we propose an anonymous authentication scheme for authenticating both pseudonyms and trust levels to support trustworthy PSN with privacy preservation. The scheme achieves secure anonymous authentication with anonymity and conditional traceability on the basis of a trusted authority (TA). By applying a back-up solution, it can guarantee communications among nodes for an extended time period even when the TA is not available. In addition, the use of batch-signature verification further reduces the cost of authenticity verification of a large number of messages. Performance analysis and evaluation further prove that the proposed scheme is effective with regard to privacy preservation, computation complexity, communication cost, flexibility, reliability, and scalability.