Salt and drought stresses are major environmental conditions that severely limit grape growth and productivity, while exogenous melatonin can alleviate the drought and salt damage to grapevines. N-acetylserotonin methyltransferase (ASMT) is the key enzyme in melatonin synthesis, which plays a critical role in regulating stress responses. However, the roles of ASMTs from grapevine under drought and salt stresses responses remain largely unclear. In this study, the VvASMT1 gene was isolated from grapevine, and its physiological functions in salt and mimic drought stress tolerance were investigated. Expression pattern analysis revealed that VvASMT1 was significantly induced by different salt and osmotic stresses. Ectopic expression of VvASMT1 in Nicotiana benthamiana significantly enhanced melatonin production in transgenic plants. Compared with wild-type plants, the transgenic lines exhibited a higher germination ratio, longer root length, lower degree of leaf wilting and relative water content (RWC) under salt and osmotic stresses. In addition, under salt and osmotic stresses, overexpression of VvASMT1 improved proline and malondialdehyde (MDA) contents, increased the activity of antioxidant enzymes and decreased the accumulation of reactive oxygen species (ROS). Taken together, our results demonstrate the explicit role of VvASMT1 in salt and osmotic stress responses, which provides a theoretical foundation for the genetic engineering of grapevine.