The interplay among microRNAs (miRNAs) plays an important role in the developments of complex human diseases. Co-expression networks can characterize the interactions among miRNAs. Differential correlation network is a powerful tool to investigate the differences of co-expression networks between cases and controls. To construct a differential correlation network, the Fisher's Z-transformation test is usually used. However, the Fisher's Z-transformation test requires the normality assumption, the violation of which would result in inflated Type I error rate. Several bootstrapping-based improvements for Fisher's Z test have been proposed. However, these methods are too computationally intensive to be used to construct differential correlation networks for high-throughput genomic data. In this article, we proposed six novel robust equal-correlation tests that are computationally efficient. The systematic simulation studies and a real microRNA data analysis showed that one of the six proposed tests (ST5) overall performed better than other methods.