MicroRNA (miRNA) regulates gene expression by binding to specific sites in the 3'untranslated regions of its target genes. Machine learning based miRNA target prediction algorithms first extract a set of features from potential binding sites (PBSs) in the mRNA and then train a classifier to distinguish targets from non-targets. However, they do not consider whether the PBSs are functional or not, and consequently result in high false positive rates. This substantially affects the follow up functional validation by experiments. We present a novel machine learning based approach, MBSTAR (Multiple instance learning of Binding Sites of miRNA TARgets), for accurate prediction of true or functional miRNA binding sites. Multiple instance learning framework is adopted to handle the lack of information about the actual binding sites in the target mRNAs. Biologically validated 9531 interacting and 973 non-interacting miRNA-mRNA pairs are identified from Tarbase 6.0 and confirmed with PAR-CLIP dataset. It is found that MBSTAR achieves the highest number of binding sites overlapping with PAR-CLIP with maximum F-Score of 0.337. Compared to the other methods, MBSTAR also predicts target mRNAs with highest accuracy. The tool and genome wide predictions are available at http://www.isical.ac.in/~bioinfo_miu/MBStar30.htm.