A control apparatus for a supercharged internal combustion engine, comprising: a turbo supercharger which includes, in an exhaust passage, a turbine that is operated by exhaust energy; an exhaust bypass passage which branches off from the exhaust passage at an upstream side portion of the turbine and merges with the exhaust passage at a downstream side portion of the turbine; a waste gate valve which is capable of switching an opening and closing of the exhaust bypass passage; a variable valve operating mechanism (46, 48) which is capable of changing a valve overlap period during which an opening period of an exhaust valve overlaps with an opening period of an intake valve; blow-through amount obtaining means for obtaining a blow-through amount of fresh air that blows through a combustion chamber from an intake passage to the exhaust passage; overlap period shortening means for shortening the valve overlap period so that the blow-through amount becomes equal to or smaller than a predetermined blow-through determination value when the blow-through amount is larger than the blow-through determination value; blow-through amount determination means for determining whether or not the blow-through amount is still larger than the blow-through determination value after the valve overlap period has been shortened by the overlap period shortening means; characterized by WGV control means for opening the waste gate valve when the blow-through amount is determined by the blow-through amount determination means to be still larger than the blow-through determination value, while, in order to decrease the blow-through amount, prohibiting opening of the waste gate valve until the blow-through amount is determined by the blow-through amount determination means to be still larger than the blow-through determination value. a turbo supercharger which includes, in an exhaust passage, a turbine that is operated by exhaust energy; an exhaust bypass passage which branches off from the exhaust passage at an upstream side portion of the turbine and merges with the exhaust passage at a downstream side portion of the turbine; a waste gate valve which is capable of switching an opening and closing of the exhaust bypass passage; a variable valve operating mechanism (46, 48) which is capable of changing a valve overlap period during which an opening period of an exhaust valve overlaps with an opening period of an intake valve; blow-through amount obtaining means for obtaining a blow-through amount of fresh air that blows through a combustion chamber from an intake passage to the exhaust passage; overlap period shortening means for shortening the valve overlap period so that the blow-through amount becomes equal to or smaller than a predetermined blow-through determination value when the blow-through amount is larger than the blow-through determination value; blow-through amount determination means for determining whether or not the blow-through amount is still larger than the blow-through determination value after the valve overlap period has been shortened by the overlap period shortening means; characterized by WGV control means for opening the waste gate valve when the blow-through amount is determined by the blow-through amount determination means to be still larger than the blow-through determination value, while, in order to decrease the blow-through amount, prohibiting opening of the waste gate valve until the blow-through amount is determined by the blow-through amount determination means to be still larger than the blow-through determination value.