To provide a double filtration blood purification apparatus that can be primed while generation of bubbles within each of a separating membrane in both of a blood component separator and a plasma component separator is avoided and also to provide a method of priming such blood purification apparatus. A cleansing liquid introducing passage 19 is provided, which is a passage dedicated to introduce a cleansing liquid P from a cleansing liquid supply source 57 into a plasma component separator 3 and, also, this cleansing liquid introducing passage 19 is provided with a dedicated, third pump 3. When the third and first pumps are driven in normal and reverse directions, respectively, by a controller 50, a sufficient pressure is applied to the cleansing liquid P by the third ump and the cleansing liquid P can be introduced into the plasma component separator 3.
