The method comprises providing a leukocyte-removing filter having a thickness of 9.0 mm to 9.4 mm, an air permeability pressure drop of 300 Pa to 700 Pa, and effective filtration area of 50 cm2 to 70 cm2 which comprises a flat and flexible container having an inlet port and an outlet port and a sheet-like leukocyte-removing-filter material with a thickness of 8.2 mm to 8.6 mm disposed to divide the container into an inlet-port side chamber and an outlet-port side chamber, providing a pair of volume restriction boards disposed outside of the inlet port side external surface and the outlet port side external surface of the flexible container, having the distance between the volume restriction boards at the portion where the volume restriction boards facing each other sandwich the leukocyte-removing filter being in a range from [thickness of leukocyte-removing filter+0.5 mm] to [thickness of leukocyte-removing filter+2.5 mm], and filtering blood or blood components through the leukocyte-removing filter under a pressure of 30 kPa to 50 kPa while restraining expansion of the flexible container occurring during filtration by means of the volume restriction boards.