An oil supply device for an internal combustion engine includes: a variable displacement pump (1) that varies a discharge pressure at which oil is discharged; an oil passage (2) through which the oil discharged from the pump (1) flows; an oil filter (3) and an oil cooler (4) each of which is arranged in the oil passage (2); a bypass passage (5) connected to the oil passage (2) and bypassing the oil cooler (4); and a bypass valve (6) that opens and closes the bypass passage (5) according to a pressure of the oil. The bypass valve (6) is operated to control the flow of the oil through the oil cooler 4 as the discharge pressure of the pump (1) is adjusted according to operating conditions of the internal combustion engine.