In most higher plants, sucrose is the significant form of carbohydrate for long-distance transportation. Sucrose transporters/sucrose carriers (SUTs/SUCs) are involved in the loading and unloading of sucrose in phloem and play an important role in the growth and development of plants. In this study, 12 RsSUC genes were first identified from the radish genome, and their phylogenetic relationships, gene structure, and conserved motifs were further analyzed. RT-qPCR results indicated that RsSUC genes exhibited various expression patterns in different tissues and development stages of the radish. Overexpression of RsSUC1b in Arabidopsis significantly improved the uptake efficiency of exogenous sucrose, and promoted leaves and lateral root growth. In addition, the transgenic plants flowered significantly earlier than wild-type (WT) plants, and the soluble sugar contents (SSCs) including sucrose, glucose, and fructose in the mature leaves and pods were increased. It could be inferred that RsSUC1b is a plasma membrane sucrose transporter and plays a vital role in sucrose transportation and sugar accumulation during plant growth and development. These findings provided novel insights into the biological function of RsSUC genes and facilitate dissecting the molecular mechanism underlying sugar transport during radish development.