Histone methylation is associated with oocyte maturation in several species and is also expected in goat oocytes, while the mechanism is still unclear. Therefore, single-cell RNA sequencing (scRNA-seq) was performed on goat germinal vesicle (GV) and metaphase II (MII) oocytes, and the functions of lysine-specific histone demethylase 1A (LSD1), one of the differentially expressed genes (DEGs) were investigated during in vitro maturation (IVM) of goat oocytes. Through scRNA-seq, 4516 DEGs were identified from GV oocytes and MII oocytes in goats, among which there were 16 histone methyltransferase and demethylase DEGs (including LSD1). The functions of LSD1 during IVM of goat oocytes were investigated through its inhibitor, GSK-LSD1. We found that the first polar body extrusion rate of goat oocytes significantly reduced with an increase in GSK-LSD1 concentration supplemented into IVM medium (0 μM: 58.84 ± 0.95%; 2.5 μM: 52.14 ± 0.51%, P < 0.01; 50 μM: 41.22 ± 0.42%, P < 0.001; 100 μM: 29.78 ± 1.78%, P < 0.001). Moreover, compared with the control group, the level of H3K4me2 methylation and p-H2AX in goat oocytes significantly increased (P < 0.001 and P < 0.01, respectively) upon 50-μM GSK-LSD1 treatment for 12 h. Furthermore, abnormalities in spindle assembly (25.94 ± 1.02% vs. 71.15 ± 3.32%; P < 0.01) and chromosome alignment (22.93 ± 1.11% vs. 76.03 ± 3.25%; P < 0.01) were observed, and cytoskeletal organization (15.31 ± 1.60% vs. 67.50 ± 3.09%; P < 0.001) was disrupted upon treatment with 50-μM GSK-LSD1 for 12 h, which compared with that in the control group. Additionally, the ratio of BCL2:BAX significantly higher (P < 0.01) in oocytes with 50-μM GSK-LSD1 treatment than that in control group. Collectively, these results indicate the important role of LSD1 in meiotic maturation of goat oocytes. Our data not only clarify dynamic changes in mRNA during oocyte maturation but also provide a theoretical basis and technical means for further studies of meiotic maturation of goat oocytes.