Trust is one of the most important factors for participants' decision-making in Online Social Networks (OSNs). The trust network from a source to a target without any prior interaction contains some important intermediate participants, the trust relations between the participants, and the social context, each of which has an important influence on trust evaluation. Thus, before performing any trust evaluation, the contextual trust network from a given source to a target needs to be extracted first, where constraints on the social context should also be considered to guarantee the quality of extracted networks. However, this problem has been proved to be NP-Complete. Towards solving this challenging problem, we first propose a complex contextual social network structure which considers social contextual impact factors. These factors have significant influences on both social interaction between participants and trust evaluation. Then, we propose a new concept called QoTN (Quality of Trust Network) and a social context-aware trust network discovery model. Finally, we propose a Social Context-Aware trust Network discovery algorithm (SCAN) by adopting the Monte Carlo method and our proposed optimization strategies. The experimental results illustrate that our proposed model and algorithm outperform the existing methods in both algorithm efficiency and the quality of the extracted trust network.