Histone methylation plays an important regulatory role in the drought response of many plants, but its regulatory mechanism in the drought response of the tea plant remains poorly understood. Here, drought stress was shown to induce lower relative water content and significantly downregulate the methylations of histone H3K4 in the tea plant. Based on our previous analysis of the SET Domain Group (SDG) gene family, the full-length coding sequence (CDS) of CsSDG36 was cloned from the tea cultivar ‘Fuding Dabaicha’. Bioinformatics analysis showed that the open reading frame (ORF) of the CsSDG36 gene was 3138 bp, encoding 1045 amino acids and containing the conserved structural domains of PWWP, PHD, SET and PostSET. The CsSDG36 protein showed a close relationship to AtATX4 of the TRX subfamily, with a molecular weight of 118,249.89 Da, and a theoretical isoelectric point of 8.87, belonging to a hydrophilic protein without a transmembrane domain, probably located on the nucleus. The expression of CsSDG36 was not detected in the wild type, while it was clearly detected in the over-expression lines of Arabidopsis. Compared with the wild type, the over-expression lines exhibited lower hyperosmotic resistance by accelerating plant water loss, increasing reactive oxygen species (ROS) pressure, and increasing leaf stomatal density. RNA-seq analysis suggested that the CsSDG36 overexpression caused the differential expression of genes related to chromatin assembly, microtubule assembly, and leaf stomatal development pathways. qRT-PCR analysis revealed the significant down-regulation of stomatal development-related genes (BASL, SBT1.2(SDD1), EPF2, TCX3, CHAL, TMM, SPCH, ERL1, and EPFL9) in the overexpression lines. This study provides a novel sight on the function of histone methyltransferase CsSDG36 under drought stress.