A cooling system for an internal combustion engine, the cooling system being applied to the internal combustion engine including a cylinder head and a cylinder block, the cooling system being configured to cool the cylinder head and the cylinder block with the use of coolant, the cooling system comprising: a first coolant passage provided in the cylinder head; a second coolant passage provided in the cylinder block; a pump configured to circulate the coolant; a radiator configured to cool the coolant; a third coolant passage (53, 55) connecting a third end of the second coolant passage to a pump outlet port, the pump outlet port being a coolant outlet port of the pump; a connection switching mechanism (53, 54, 62, 584, 78) configured to switch a status of pump connection between a forward flow connection state and a reverse flow connection state, the status of pump connection being a status of connection of the pump to a first end of the first coolant passage, the forward flow connection state being a state where the first end of the first coolant passage is connected to the pump outlet port, the reverse flow connection state being a state where the first end of the first coolant passage is connected to a pump inlet port, the pump inlet port being a coolant inlet port of the pump; a fourth coolant passage (56, 57) connecting a second end of the first coolant passage to a fourth end of the second coolant passage; a fifth coolant passage connecting the fourth coolant passage to the pump inlet port; and a shutoff valve located in the fifth coolant passage and configured to open the fifth coolant passage when the shutoff valve is in a valve open position and shut the fifth coolant passage when the shutoff valve is in a valve closed position, wherein: the radiator is disposed at a location at which coolant that flows out from the first end of the first coolant passage and that flows into the third end of the second coolant passage via the connection switching mechanism (53, 55, 62, 584, 78) is not cooled, and at a location at which coolant that flows out from the second end of the first coolant passage and the fourth end of the second coolant passage is cooled at the time when the forward flow connection state is established. a first coolant passage provided in the cylinder head; a second coolant passage provided in the cylinder block; a pump configured to circulate the coolant; a radiator configured to cool the coolant; a third coolant passage (53, 55) connecting a third end of the second coolant passage to a pump outlet port, the pump outlet port being a coolant outlet port of the pump; a connection switching mechanism (53, 54, 62, 584, 78) configured to switch a status of pump connection between a forward flow connection state and a reverse flow connection state, the status of pump connection being a status of connection of the pump to a first end of the first coolant passage, the forward flow connection state being a state where the first end of the first coolant passage is connected to the pump outlet port, the reverse flow connection state being a state where the first end of the first coolant passage is connected to a pump inlet port, the pump inlet port being a coolant inlet port of the pump; a fourth coolant passage (56, 57) connecting a second end of the first coolant passage to a fourth end of the second coolant passage; a fifth coolant passage connecting the fourth coolant passage to the pump inlet port; and a shutoff valve located in the fifth coolant passage and configured to open the fifth coolant passage when the shutoff valve is in a valve open position and shut the fifth coolant passage when the shutoff valve is in a valve closed position, wherein: the radiator is disposed at a location at which coolant that flows out from the first end of the first coolant passage and that flows into the third end of the second coolant passage via the connection switching mechanism (53, 55, 62, 584, 78) is not cooled, and at a location at which coolant that flows out from the second end of the first coolant passage and the fourth end of the second coolant passage is cooled at the time when the forward flow connection state is established.