A liquid pump dispenser includes a vial adapter connected with a pump dispenser unit including a piston-type dispenser pump. When the vial adapter is coupled to the neck of a medical vial by latching, a piercing mandrel pierces a stopper sealing the vial. A fluid-tight communication between the vial adapter and pump dispenser unit is established by a flexible connecting tube, which helps to compensate mechanical tolerances and any misalignment or between the vial adapter and pump dispenser unit during assembly or use. The liquid pump dispenser can be used in an upside-down orientation of the medical vial without problems such as leakage or dripping at an outlet nozzle, and ensures a precise dosage of the liquid pumped from the medical vial. The vial adapter together with the pump dispenser unit can be pre-assembled and packaged as a unit.