A bacterium producing non-or partially digestible dextran was isolated from kimchi broth by enrichment culture technique. The bacterium was identified tentatively as Leuconostoc sp. strain SKY. We established the response surface methodology (Box-Behnken design) to optimize the principle parameters such as culture pH, temperature, and yeast extract concentration for maximizing production of dextran. The ranges of parameters were determined based on prior screening works done at our laboratory and accordingly chosen as 5.5, 6.5, and 7.5 for pH, 25, 30, and 35 o C for temperature, and 1, 5, and 9 g/l yeast extract. Initial concentration of sucrose was 100 g/l. The mineral medium consisted of 3.0 g KH2PO4, 0.01 g FeSO4․ H2O, 0.01 g MnSO4․4H2O, 0.2 g MgSO4․7H2O, 0.01 g NaCl, and 0.05 g CaCO3 per 1 liter deionized water. The optimum values of pH and temperature, and yeast extract concentration were obtained at pH (around 7.0), temperature (27 to 28 o C), and yeast extract (6 to 7 g/l). The best dextran yield was 60% (dextran/g sucrose). The best dextran productivity was 0.8 g/h-l.