A piston pump includes a first piston pump including a first piston and a
first pump chamber, a second piston pump including a second piston and a
second pump chamber, the second piston operating to follow the first
piston, a pressure release passage formed in communication with the
second pump chamber, and a relief valve provided at the pressure release
passage and defining an upper limit discharge pressure of the second
piston pump. When a discharge pressure of the second piston pump is equal
to or smaller than the upper limit, a discharge fluid of the second
piston pump is added to that of the first piston pump so as to flow into
an outlet port. When the discharge pressure exceeds the upper limit, the
discharge fluid is released to the pressure release passage and the
discharge fluid of the first piston pump only flows to the outlet port.