During the last decade, with the advent of inexpensive microarray and RNA-seq technologies, there have been many expression quantitative trait loci (eQTL) studies for identifying genetic variants called eQTLs that regulate gene expression. Discovering eQTLs has been increasingly important as they may elucidate the functional consequence of non-coding variants identified from genome-wide association studies. Recently, several eQTL studies such as the Genotype-Tissue Expression (GTEx) consortium have made a great effort to obtain gene expression from multiple tissues. One advantage of these multi-tissue eQTL datasets is that they may allow one to identify more eQTLs by combining information across multiple tissues. Although a few methods have been proposed for multi-tissue eQTL studies, they are often computationally intensive and may not achieve optimal power because they do not consider a biological insight that a genetic variant regulates gene expression similarly in related tissues. In this paper, we propose an efficient meta-analysis approach for identifying eQTLs from large multi-tissue eQTL datasets. We name our method RECOV because it uses a random effects (RE) meta-analysis with an explicit covariance (COV) term to model the correlation of effect that eQTLs have across tissues. Our approach is faster than the previous approaches and properly controls the false-positive rate. We apply our approach to the real multi-tissue eQTL dataset from GTEx that contains 44 tissues, and show that our approach detects more eQTLs and eGenes than previous approaches.