A high-pressure pump having a pump housing in which a plurality of pump elements are disposed, and by means of which fluid is pumped at high pressure via a high-pressure conduit system to a common high-pressure connection. The pump housing has a housing body and for each pump element one housing cap covering the pump element and joined to the housing body. The high-pressure conduit system has high-pressure bores extending without intersections in the housing body which bores are joined together in the region of the transition from the housing body to one of the housing caps, or in one of the housing caps, to form the common high-pressure connection.