Rising fluid velocity in the fiber tubes of a hollow-fiber module has two conflicting effects. One, the decrease in resistance to permeation due to reduction in concentration polarization, is good for ultrafiltration, while the other, the decrease in average transmembrane pressure due to increase in frictional pressure loss, is bad for ultrafiltration. It appears, therefore, that proper adjustment of fluid velocity as well as proper arrangement of the number of fiber passes in a hollow-fiber module of fixed total hollow fibers, might effectively suppress the undesirable resistance to permeation while still preserving an effective transmembrane pressure and thereby lead to improved performance of membrane ultrafiltration. It was found that considerable improvement in ultrafiltration is obtainable by employing a multipass hollow-fiber membrane module rather than using the one with only single fiber pass and with the same total fibers, especially for a dilute solution ultrafiltered with low volumetric flow rate and under high transmembrane pressure.