A blood purification apparatus comprising: a blood purifier which includes a blood purification membrane and performs blood purification in the blood purification membrane; an arterial blood circuit, a proximal end of which is connected to the blood purifier, a blood pump being disposed in the arterial blood circuit; a venous blood circuit, a proximal end of which is connected to the blood purifier; a dialysate introduction line which introduces a dialysate into the blood purifier; a dialysate discharge line which discharges the dialysate from the blood purifier; a substitution line, an end of which is connected to a substitution source, and the other end of which is connected to the arterial blood circuit; and a substitution supplying device capable of supplying substitution flowing in the substitution line to the arterial blood circuit, wherein the apparatus further includes a control device capable of assuming or measuring a blood concentration of a dilution channel section formed by a channel from a connection part with the substitution line in the arterial blood circuit to the blood purifier and capable of controlling the flow rate of the substitution supplied by the substitution supplying device based on the assumed or measured blood concentration, characterized in that the apparatus further comprises: a calculation device, configured to calculate a time when blood diluted by the supplying of the substitution to the dilution channel section reaches the blood purifier and to assume the blood concentration of the dilution channel section, wherein the control device is configured to control the flow rate of the substitution supplied by the substitution supplying device depending on the blood concentration assumed by the calculation device. a blood purifier which includes a blood purification membrane and performs blood purification in the blood purification membrane; an arterial blood circuit, a proximal end of which is connected to the blood purifier, a blood pump being disposed in the arterial blood circuit; a venous blood circuit, a proximal end of which is connected to the blood purifier; a dialysate introduction line which introduces a dialysate into the blood purifier; a dialysate discharge line which discharges the dialysate from the blood purifier; a substitution line, an end of which is connected to a substitution source, and the other end of which is connected to the arterial blood circuit; and a substitution supplying device capable of supplying substitution flowing in the substitution line to the arterial blood circuit, wherein the apparatus further includes a control device capable of assuming or measuring a blood concentration of a dilution channel section formed by a channel from a connection part with the substitution line in the arterial blood circuit to the blood purifier and capable of controlling the flow rate of the substitution supplied by the substitution supplying device based on the assumed or measured blood concentration, characterized in that the apparatus further comprises: a calculation device, configured to calculate a time when blood diluted by the supplying of the substitution to the dilution channel section reaches the blood purifier and to assume the blood concentration of the dilution channel section, wherein the control device is configured to control the flow rate of the substitution supplied by the substitution supplying device depending on the blood concentration assumed by the calculation device. a calculation device, configured to calculate a time when blood diluted by the supplying of the substitution to the dilution channel section reaches the blood purifier and to assume the blood concentration of the dilution channel section, wherein the control device is configured to control the flow rate of the substitution supplied by the substitution supplying device depending on the blood concentration assumed by the calculation device.