An electromagnetic reciprocating pump which maintains the outlet pressure at a preset value comprising a pressure sensor for detecting the actual outlet pressure of the electromagnetic reciprocating pump and means to feedback control the frequency of the reciprocating motion and, if necessary, its stroke of the electromagnetic drive means based on the deviation from the preset outlet pressure of the actual outlet pressure. The reciprocating motion frequency control of the electromagnetic drive means may be done by modulating the frequency and amplitude of the half-wave AC current supplied to the electromagnetic drive means. With this, the control of the number of times of the reciprocating motion of the electromagnetic drive means can be carried out without changing the reciprocating motion stroke of the electromagnetic drive means.