Online social networks are becoming increasingly popular and are being used as the means for a variety of rich activities. This demands the evaluation of the trustworthiness between two unknown participants along a certain social trust path between them in the social network. However, there are usually many social trust paths between participants. Thus, a challenging problem is finding which social trust path is the optimal one that can yield the most trustworthy evaluation result. In this paper, we first present a new complex social network structure and a new concept of Quality of Trust (QoT) to illustrate the ability to guarantee a certain level of trustworthiness in trust evaluation. We then model the optimal social trust path selection as a Multi-Constrained Optimal Path (MCOP) selection problem which is NP-Complete. For solving this problem, we propose an efficient approximation algorithm MONTE K based on the Monte Carlo method. The results of our experiments conducted on a real dataset of social networks illustrate that our proposed algorithm significantly outperforms existing approaches in both efficiency and the quality of selected social trust paths.