A pump, having a pump housing with an impeller arranged therein, features an anti-airlock valve assembly configured with a valve housing having a passageway configured with a vent hole to allow air to bleed out of the pump housing into the atmosphere so liquid can fill the pump housing, rise and engage the impeller in order to get the pump running; and a valve ball arranged in the passageway, the valve ball configured to rest against one part of the passageway so air can pass out of the vent hole, and also configured to be light or buoyant enough to respond to the liquid filling the pump housing, float upwardly and rest against another part of the passageway so as not to allow water to escape readily from the vent hole after the liquid rises to a sufficient level and substantially engages the impeller.