System and method of controlling fuel cell system using a drain-purge valve

A system and method of controlling fuel cell system is provided that simultaneously drains condensation and purges hydrogen via single valve. In particular, condensate water is drained by opening a drain-purge valve at a point in time at which a production amount of the condensate water exceeds a capacity of a water trap. An opening time of the drain-purge valve is then determined depending on a hydrogen concentration of an anode side and a target hydrogen concentration after the draining the condensate water. Hydrogen is then purged by maintaining the drain-purge valve in a state in which it is opened for the determined opening time.