It was shown that AEDG peptide (Ala-Glu-Asp-Gly, Epitalon) regulates the function of the pineal gland, the retina, and the brain. AEDG peptide increases longevity in animals and decreases experimental cancerogenesis. AEDG peptide induces neuronal cell differentiation in retinal and human periodontal ligament stem cells. The aim of the study was to investigate the influence of AEDG peptide on neurogenic differentiation gene expression and protein synthesis in human gingival mesenchymal stem cells, and to suggest the basis for the epigenetic mechanism of this process. AEDG peptide increased the synthesis of neurogenic differentiation markers: Nestin, GAP43, β Tubulin III, Doublecortin in hGMSCs. AEDG peptide increased Nestin, GAP43, β Tubulin III and Doublecortin mRNA expression by 1.6–1.8 times in hGMSCs. Molecular modelling method showed, that AEDG peptide preferably binds with H1/6 and H1/3 histones in His-Pro-Ser-Tyr-Met-Ala-His-Pro-Ala-Arg-Lys and Tyr-Arg-Lys-Thr-Gln sites, which interact with DNA. These results correspond to previous experimental data. AEDG peptide and histones H1/3, H1/6 binding may be one of the mechanisms which provides an increase of Nestin, GAP43, β Tubulin III, and Doublecortin neuronal differentiation gene transcription. AEDG peptide can epigenetically regulate neuronal differentiation gene expression and protein synthesis in human stem cells.