As one of the key enzymes in the biosynthesis of polyamines, S-adenosylmethionine decarboxylase (SAMDC) plays an important role in plant stress resistance. In this study, four SAMDC genes (CsSAMDC1-4) were identified in cucumber (Cucumis sativus L.) and divided into three groups (I, II, and III) by phylogenetic analysis. Motif analysis suggested the existence of many conserved motifs, which is compatible with SAMDC protein classification. Gene structure analysis revealed that CsSAMDC2 and CsSAMDC3 in group I have no intron, which showed a similar response to salt stress by gene expression analysis. CsSAMDC3 responded differently to hormone and stress treatments, and was more susceptible to salt stress. Compared with wild-type (WT) tobacco, the activities of superoxide dismutase, peroxidase, and catalase were increased in CsSAMDC3-overexpressing tobacco under salt stress, but the content of electrolyte leakage, malondialdehyde, and hydrogen peroxide were decreased, which alleviated the inhibition of growth induced by salt stress. Under salt stress, overexpression of CsSAMDC3 in transgenic tobacco plants exhibited salt tolerance, mainly in the form of a significant increase in dry and fresh weight, the maximal quantum yield of PSII photochemistry, the net photosynthetic rate and the content of spermidine and spermine, while the content of putrescine was reduced. In addition, the expression levels of antioxidase-related coding genes (NtSOD, NtPOD, NtCAT) and PAs metabolism-related coding genes (NtSAMS, NtSPDS, NtSPMS, NtPAO) in transgentic plants was lower than WT under salt stress, which suggested that overexpression of CsSAMDC3 affected the expression of these genes. In summary, our results showed that CsSAMDC3 could be used as a potential candidate gene to improve salt tolerance of cucumber by regulating polyamine and antioxidant metabolism.