A plunger pump for supplying solution in accordance with an extrusion action of a plunger within a pump chamber. The plunger pump includes a cleaning chamber sealed by a seal member around and relative to the plunger, with a cleaning liquid inlet-side flow conduit and a cleaning liquid outlet-side flow conduit for communicating with the cleaning chamber, respectively. A mechanism isolates one of the inlet- and outlet-side flow conduits from the atmosphere and releases the other to an atmosphere under a condition where the cleaning liquid inlet- or outlet-side flow conduits are filled with the cleaning liquid. If the seal member in sliding contact with the plunger is degraded or aged, it is possible to observe a leakage of the liquid from the pump chamber along a sealing face between the seal member and the plunger.
