Intake air flow rate control means having a control valve and a stepping motor for driving the control valve is arranged in a passage other than a passage in which a throttle valve is disposed. In a fast idling control mode (when a coolant temperature is below 70.degree. C., for example) and a hot idling control mode (when the coolant temperature is above 70.degree. C., for example), the control valve is driven by the stepping motor to control an engine idling rotational speed. The numbers of steps of the stepping motor for given coolant temperatures, which are to be used in the fast idling control mode, are previously stored as tables ST1.about.ST3. A converted value ISTA of steps corresponding to a target rotational speed is calculated based on a predetermined conversion expression. An arithmetic operation is carried out such that the number of steps ISTEP, which was learnt in the previous hot idling control mode and stored in a permanently powered memory, is equal to the converted value ISTA. In the fast idling control mode, prior to the feedback control of the control valve, the number of steps of the stepping motor ST for the given coolant temperature is corrected based on the number of steps ISTEP stored in the memory. The stepping motor is controlled by the corrected number of steps ST1A.about.ST3A.