Inspired by the importance of social media, a Social Network Opinion Leaders (SNOL) system has been proposed in this paper. The purpose of this system is to identify topic-based opinion leaders of social media. In order to accomplish this goal, several steps have been taken, such as data collection, data processing, data analysis, data classification, ranking of topic-based opinion leaders, and evaluation. The SNOL system has two main parts. In the first part, collected tweets are classified by semantic kernels for topic-based analysis. In the second part, leadership scores are given to each user in the network according to topic modeling and user modeling results. Leadership scores are then calculated with the formula generated and opinion leaders are determined for each category. Experiments are performed on data gathered from Twitter including 17,234,924 tweets from 38,727 users. The evaluation of opinion leader detection is a difficult job since there is no standard method for identifying opinion leaders. Therefore, the evaluation of the results of this study has been done using two different methods, retweet count and spread score, to prove that the suggested methodology outperforms the PageRank algorithm. The results have also been evaluated considering the user-topic sentiment correlation of the retrieved lists. Furthermore, SNOL has been compared against some opinion leader detection methods previously presented in the literature. The experimental results show that SNOL generates remarkably higher performance than the PageRank algorithm and other existing algorithms in the literature for nearly all topics and all selected top N opinion leaders.