Provided is a control device for an engine which is capable of purifying NOx with high efficiency at a restart after an idle stop without deteriorating purification efficiency of HC and CO. At the restart after the idle stop, an air-fuel ratio is controlled to be rich, and an atmosphere inside of a catalyst is estimated on the basis of a required time ΔT from a time point at which an output value (VO2—2) of first oxygen concentration detection means upstream of the catalyst exceeds a predetermined value A1 to a time point at which an output value (VO2—2) of second oxygen concentration detection means downstream of the catalyst exceeds a predetermined value A2, whereby an air-fuel ratio at next and subsequent restarts is corrected so that the atmosphere inside of the catalyst is optimized at the next and subsequent restarts.