An iminodiacetate (IDA) group as a chelate-forming group was introduced uniformly throughout a porous polyethylene membrane of a hollow-fiber form. The binary metal ions (Co2+ and Cu2+) were transported to the IDA group by convection by permeating the aqueous solution outwards at a residence time of 1.7 s through the chelating porous membrane whose thickness was 0.85 mm. The time course of the concentration profile of the metals sorbed across the membrane during permeation was determined along with the determination of the breakthrough curves. At an initial stage, both metal ions were quantitatively sorbed onto the membrane, where the copper ion occupied the inner part and the cobalt ion occupied the outer part, and while the effluent volume increased, the Cu ion with a high affinity for the IDA group displaced the initially sorbed Co, and finally, occupied almost all of the IDA groups. Negligible diffusional mass-transfer resistance of Co and Cu ions to the IDA group and instantaneous displacement of the sorbed Co with Cu ion were demonstrated in the permeation mode.