Leymus chinensis is an important perennial forage grass natively distributed in the Eurasian Steppe. However, little is known about the molecular mechanism of its adaptation to extreme environmental conditions. Based on L. chinensis cold-treated sequence database, a highly expressed S-adenosylmethionine decarboxylase gene (LcSAMDC1) was isolated from L. chinensis. Gene structure analysis showed that LcSAMDC1 has two introns and three exons as well as three non-overlapping ORFs in its mRNA sequence. One hour of cold exposure caused a significant up-regulation of LcSAMDC1, while abscisic acid (ABA), salt, and osmotic stresses slightly induced its expression. Analysis of gene expression in different tissues showed that LcSAMDC1 was expressed ubiquitously, with higher levels in the young spike and rhizome. Overexpression of the main ORF of LcSAMDC1 in transgenic Arabidopsis promoted increased tolerance to cold and salt stress relative to wild type Arabidopsis. The concentration of polyamines, proline, and chlorophyll was significantly higher in transgenic Arabidopsis, and spermine of polyamines increased more under cold than under salt stress. These results suggest that LcSAMDC1 was induced in response to cold and could influence the production of polyamines involved in stress tolerance of L. chinensis. Moreover, transgenic expression of LcSAMDC1 could be used to improve the abiotic resistance of crops.