In many real world applications, the same item may be described by multiple sources. As a consequence, conflicts among these sources are inevitable, which leads to an important task: how to identify which piece of information is trustworthy, i.e., the truth discovery task. Intuitively, if the piece of information is from a reliable source, then it is more trustworthy, and the source that provides trustworthy information is more reliable. Based on this principle, truth discovery approaches have been proposed to infer source reliability degrees and the most trustworthy information (i.e., the truth) simultaneously. However, existing approaches overlook the ubiquitous long-tail phenomenon in the tasks, i.e., most sources only provide a few claims and only a few sources make plenty of claims, which causes the source reliability estimation for small sources to be unreasonable. To tackle this challenge, we propose a confidence-aware truth discovery (CATD) method to automatically detect truths from conflicting data with long-tail phenomenon. The proposed method not only estimates source reliability, but also considers the confidence interval of the estimation, so that it can effectively reflect real source reliability for sources with various levels of participation. Experiments on four real world tasks as well as simulated multi-source long-tail datasets demonstrate that the proposed method outperforms existing state-of-the-art truth discovery approaches by successful discounting the effect of small sources.