A liquid feed pump system having a pump for feeding a liquid stored on the suction side thereof to the discharge side, resisting a flow resistance from a discharge-side flow resistance element. A first passage connects the flow resistance element and the pump, and a second passage is formed in the first passage. The second passage has a gas-flow resistance smaller than that of the flow resistance element. At the start of pump operation, gas in the pump is quickly discharged through the second passage, so that the liquid can be fed without a delay. The second passage may be an orifice, which is bored through the wall of the first passage and opens to the atmosphere at all times, or a by-pass, which makes a detour around the discharge-side flow resistance element and continually connects the upper and lower courses of the resistance element.