An oil passage extending from an oil pump to a discharge port in an internal combustion engine is, at its halfway point, branched into at least two oil passages, for example, a first oil passage and a second oil passage. One of the at least two branched oil passages, for example, the second oil passage is provided with a restricting portion configured as a first orifice for restricting a flow amount of oil by reducing a diameter of the first orifice. A bypass valve is provided which acts, when a hydraulic pressure in the second oil passage exceeds a specific value, to bypass the first orifice so as to increase the flow rate of oil. It is possible to increase the hydraulic pressure at the time of low speed rotation up to a necessary pressure only by providing the restricting portion, without enhancing the performance of the oil pump. Accordingly, it is possible to suppress the increase in weight and cost of the lubricating system as compared with the prior art lubricating system in which the performance of the oil pump is enhanced, and since it is not required to increase the rotational speed of the oil pump, it is possible to prevent the loss in output of the internal combustion engine due to the increased friction of the oil pump. Further, it is possible to prevent an excessive increase in pressure of the oil passage by the effect of the bypass valve.