A control apparatus comprising an air-fuel ratio sensor disposed between the exhaust gas aggregated portion and the three-way catalyst, and which outputs an output value corresponding to an amount of oxygen and an amount of unburnt substances that has reached the exhaust-gas-side electrode layer via the porous; an actual detected air-fuel ratio obtaining section which obtains an actual detected air-fuel ratio by converting an actual output value of the air-fuel ratio sensor into an air-fuel ratio; and an instructed fuel injection amount calculation section which corrects the amount of the fuel injected from a plurality of the fuel injection valves so that the actual detected air-fuel ratio coincides with a target air-fuel ratio; and an air-fuel ratio imbalance indicating value obtaining section which obtains an air-fuel ratio imbalance indicating value which becomes larger as a degree of a non-uniformity among a plurality of the cylinders of cylinder-by-cylinder air-fuel ratios.