An apparatus and method for controlling operation of a fuel cell system is provided. The method includes measuring a stack current and a stack insulation resistance. The measured stack current is compared with a predetermined current reference value and the measured stack insulation resistance is compared with a predetermined first insulation reference value. An air supply amount to a fuel cell stack is increased during a predetermined time when the measured stack current is less than the predetermined current reference value and the measured stack insulation resistance is less than or equal to the predetermined first insulation reference value.