Ovarian cancer is the most lethal gynecological malignancy. The high mortality results from late diagnosis and the development of drug resistance. Drug resistance results from changes in the expression of different drug-resistance genes that may be regulated miRNA. The main aim of our study was to detect changes in miRNA expression levels in two cisplatin (CIS) and two paclitaxel (PAC)—resistant variants of the A2780 drug-sensitive ovarian cancer cell line—by miRNA microarray. The next goal was to identify miRNAs responsible for the regulation of drug-resistance genes. We observed changes in the expression of 46 miRNA that may be related to drug resistance. The overexpression of miR-125b-5p, miR-99a-5p, miR-296-3p, and miR-887-3p and downregulation of miR-218-5p, miR-221-3p, and miR-222-3p was observed in both CIS-resistant cell lines. In both PAC-resistant cell lines, we observed the upregulation of miR-221-3p, miR-222-3p, and miR-4485, and decreased expression of miR-551b-3p, miR-551b-5p, and miR-218-5p. Analysis of targets suggest that expression of important drug-resistant genes like protein Tyrosine Phosphatase Receptor Type K (PTPRK), receptor tyrosine kinase—EPHA7, Semaphorin 3A (SEMA3A), or the ATP-binding cassette subfamily B member 1 gene (ABCB1) can be regulated by miRNA.