A gradient pump apparatus which is capable of continuously and precisely feeding, to a chromatograph, eluents at intervals of certain time and at a constant flow rate in units of nano-liter per minute while the composition of two or more eluent components is changed. The gradient pump apparatus includes a 10-port valve for switching an eluent mixing pipe, in which a feed pressure of eluents changes with time, to be connected to a first loop which is supplied with another eluent from an isocratic pump that should function to hold an eluent feed pressure constant, and which is connected to an analytic section, or to a second loop through which the eluents are drained. A controller computes a difference between a value of the pressure in the eluent mixing pipe and a value of the eluent feed pressure applied from the isocratic pump when the eluent mixing pipe is connected to the second loop. At the time when the eluent mixing pipe is connected to the first loop with shift of the 10-port valve, the feed speed of the isocratic pump is determined based on the above pressure difference. The isocratic pump is controlled in sync with the valve shift so that the determined feed speed of the isocratic pump is obtained.