The NAC (NAM, ATAF1/2, CUC2) family of transcription factors (TFs) is a vital transcription factor family of plants. It controls multiple parts of plant development, tissue formation, and abiotic stress response. We cloned the FvNAC29 gene from Fragaria vesca (a diploid strawberry) for this research. There is a conserved NAM structural domain in the FvNAC29 protein. The highest homology between FvNAC29 and PaNAC1 was found by phylogenetic tree analysis. Subcellular localization revealed that FvNAC29 is localized onto the nucleus. Compared to other tissues, the expression level of FvNAC29 was higher in young leaves and roots. In addition, Arabidopsis plants overexpressing FvNAC29 had higher cold and high-salinity tolerance than the wild type (WT) and unloaded line with empty vector (UL). The proline and chlorophyll contents of transgenic Arabidopsis plants, along with the activities of the antioxidant enzymes like catalase (CAT), peroxidase (POD), and superoxide dismutase (SOD) under 200 mM NaCl treatment or −8 °C treatment, were higher than those activities of the control. Meanwhile, malondialdehyde (MDA) and the reactive oxygen species (ROS) content were higher in the WT and UL lines. FvNAC29 improves transgenic plant resistance to cold and salt stress by regulating the expression levels of AtRD29a, AtCCA1, AtP5CS1, and AtSnRK2.4. It also improves the potential to tolerate cold stress by positively regulating the expression levels of AtCBF1, AtCBF4, AtCOR15a, and AtCOR47. These findings suggest that FvNAC29 may be related to the processes and the molecular mechanisms of F. vesca response to high-salinity stress and LT stress, providing a comprehensive understanding of the NAC TFs.