Polyamines play essential roles in plant development and various stress responses. In this study, one of the cotton S-adenosylmethionine decarboxylase (SAMDC) genes, GhSAMDC1, was constructed in the pGWB17 vector and overexpressed in tobacco. Leaf area and plant height increased 25.9–36.6% and 15.0–27.0%, respectively, compared to the wild type, and flowering time was advanced by 5 days in transgenic tobacco lines. Polyamine and gene expression analyses demonstrated that a decrease in spermidine and an increase in total polyamines and spermine might be regulated by NtSPDS4 and NtSPMS in transgenic plants. Furthermore, exogenous spermidine, spermine and spermidine synthesis inhibitor dicyclohexylamine were used for complementary tests, which resulted in small leaves and dwarf plants, big leaves and early flowering, and big leaves and dwarf plants, respectively. These results indicate that spermidine and spermine are mainly involved in the vegetative growth and early flowering stages, respectively. Expression analysis of flowering-related genes suggested that NtSOC1, NtAP1, NtNFL1 and NtFT4 were upregulated in transgenic plants. In conclusion, ectopic GhSAMDC1 is involved in the conversion of spermidine to spermine, resulting in rapid vegetative growth and early flowering in tobacco, which could be applied to genetically improve plants.