Corynebacterium glutamicum is one of the well-studied industrial strain that is used for the production of nucleotides and amino acids. Recently, it has also been studied as a possible producer of organic acids such as succinic acid, based on its ability to produce organic acids under an oxygen deprivation condition. In this study, we conducted the optimization of medium components for improved succinate production from C. glutamicum under an oxygen deprivation condition by Plackett-Burman design and applied a response surface methodology. A Plackett-Burman design for ten factors such as glucose, ammonium sulfate, magnesium sulfate, potassium phosphate ($K_2HPO_4$ and $KH_2PO_4$), iron sulfate, manganese sulfate, biotin, thiamine, and sodium bicarbonate was applied to evaluate the effects on succinate production. Glucose, ammonium sulfate, magnesium sulfate, and dipotassium phosphate were found to have significant influence on succinate production, and the optimal concentrations of these four factors were sequentially investigated by the response surface methodology using a Box-Behnken design. The optimal medium components obtained for achieving maximum concentration of succinic acid were as follows: glucose 10 g/l, magnesium sulfate 0.5 g/l, dipotassium phosphate ($K_2HPO_4$) 0.75 g/l, potassium dihydrogen phosphate ($KH_2PO_4$) 0.5 g/l, iron sulfate 6 mg/l, manganese sulfate 4.2 mg/l, biotin 0.2 mg/l, thiamine 0.2 mg/l, and sodium bicarbonate 100 mM. The parameters that differed from a normal BT medium were glucose changed from 40 g/l to 10 g/l, dipotassium phosphate ($K_2HPO_4$) 0.5 g/l changed to 0.75 g/l, and ammonium sulfate ($(NH_4)_2SO_4$) 7 g/l changed to 0 g/l. Under these conditions, the final succinic acid concentration was 16.3 mM, which is about 1.46 fold higher than the original medium (11.1 mM) at 24 h. This work showed the improvement of succinate production by a simple change of media components deduced from sequential optimization.