In this study, thermal and hydraulic transient of once-through type steam generators in a small modular reactor following a change in feedwater flow is predicted. For which, the calculation code for simulating transient phase change phenomena is developed, and Chen's boiling heat transfer coefficient for two-phase region is used. During a change of feedwater flow, pressure of main steam discharged from the steam generators shows transient variation, but it does not exceed its setpoint related to safety. That is, it is verified that the designed steam generators are suitable for stable operation.