A blood collection system comprises a suction unit (11), a hose arrangement (12) connected to the suction unit, means for aspirating blood and air through the suction unit and for pumping said blood and air through the hose arrangement, a flow sensing unit (14) for continuously sensing the blood flow through the hose arrangement, an anticoagulant additive dosing system (15) for continuously dosing an anticoagulant additive into the blood flowed through the hose arrangement in response to the continuously sensed blood flow, a mixing unit (16) for mixing the blood with the anticoagulant additive dosed into the blood, and a collection vessel (17) for collecting the mixed blood and anticoagulant additive. The means for aspirating and pumping the blood and air is a pump system (13) providing a known constant volume flow of the blood and air in the hose arrangement, the flow sensing unit (14) is arranged for continuously sensing the mass flow of blood through the hose arrangement by means of continuously measuring a parameter indicative of the weight of blood in a tubing section (14a), through which the blood is transported, and the anticoagulant additive dosing system comprises a control unit (15d) connected to the flow sensing unit and arranged for automatically controlling the continuously dosing of an anticoagulant additive into the blood flowed through the hose arrangement in response to the continuously sensed mass flow of blood.