A blood purifying apparatus particularly suitable for continuous blood purification, and a method of controlling the same whereby the weight of body fluid removed from a patient and a feed weight to the patient can be more accurately controlled. A blood purifying apparatus 50 adapted for the continuous blood purification includes a drain C, a dialysate feed A, and a replacement fluid feed B, which are equipped with transfer pumps 5, 6, 7, respectively, reservoir containers 8, 9, and 10, respectively, that are capable of storing a predetermined volume, and fluid level sensors 11, 12, and 13, respectively. The blood purifying apparatus further includes a single weightmeter 20 capable of measuring the reservoir containers 8, 9, and 10 all at the same time.