The development and production of bread wheat (Triticum aestivum L.) are widely affected by drought stress worldwide. Many NAC transcription factors (TFs) of stress-associated group (SNAC) are functionally proven to regulate drought tolerance. In this study, we identified 41 TaSNACs that were classified into 14 groups, and the expression of TaSNAC4-3D was induced in the leaf tissue via osmotic or abscisic acid (ABA) treatment. TaSNAC4-3D was localized to the nucleus through the transient expression assay, and the C-terminal region exhibited transcriptional activity via transactivation assays. TaSNAC4-3D was overexpressed in common wheat. The wheat plants with TaSNAC4-3D overexpression was more sensitive to drought stress compared with wild-type (WT) plants. The water loss rate showed no difference between transgenic lines and WT plants. However, drought stress increased H2O2 and O2– accumulation and promoted programmed cell death (PCD) in the leaf tissue of TaSNAC4-3D overexpression lines compared with WT plants. RNA-seq analysis was performed under well-watered and drought conditions, and four strong potential target genes, encoding senescence regulators, were identified by analyzing their promoters containing the NAC recognition sequence (NACRS). Based on these results, our findings revealed that TaSNAC4-3D negatively regulates drought tolerance by inducing oxidative damage in bread wheat.