To comply with a wide range of operating conditions, in a nonpulsation pump having a plurality of reciprocating pumps and keeping a combined discharge flow rate obtained by combining the discharge rates of the reciprocating pumps constant.

A plunger 16 for each reciprocating pump 12 performs compensation movement reducing pump chamber volume before a delivery period in order to compensate a reduction in the discharge flow rate caused when delivery is started. If the pump chamber volume is not appropriately compensated by the compensation movement, pulsation is caused in a delivery pipe 34. The pulsation is detected with a pressure sensor 38. Based on the detected pressure, a pressure regulating valve 36 is regulated so that, when the delivery is started, the reduction in the discharge flow rate and the reduced amount of the pump chamber volume through the compensation movement become equal to each other, that is, the pulsation is not caused.