A apparatus for an engine, and the apparatus includes an ECU. The ECU is configured to (i) perform a feedback control such that the engine speed converges to a target speed by correcting ignition timing during the feedback control, (ii) make a determination that fuel supplied to the engine is a heavy fuel when an ignition fulfillment rate is equal to or greater than a predetermined threshold value within a predetermined period after the engine is started, the ignition fulfillment rate is a ratio of the advance correction amount of the ignition timing to a maximum ignition correction range, the maximum ignition correction range is a maximum range in which the ignition timing is corrected during the feedback control, and (iii) set the threshold value to a value that depends on a temperature representative value of the engine, the temperature representative value is correlated with the engine temperature.