Apparatus for withdrawing blood from a donor, comprising a blood line (5) forming part of the blood flow conduit means for conducting the blood withdrawn from the donor. To the blood line (5) there are further connected a pressure transducer (6) and a blood pump (7). The pressure transducer (6) has a visual display (10) for reading the actual pressure P A at the exit of the needle (2). Along a signal line (11), the transducer (6) supplies to a control device (8) an electric signal representing the pressure P A . Moreover, the blood pump (7) co-operates with means for measuring the blood flow rate of the pump. The electric signal representing the measured blood flow rate is supplied to the control device (8) by means of a signal line (13). Said control device serves to control the flow rate of the blood pump (7) in response to the actual values of the pressure P A and the blood flow rate Q. The control device (8) operates according to a certain control algorithm in such a way that during the withdrawal procedure the pump (7) withdraws an optimal amount of blood per unit time from the donor.