In this work, Co(II) and Ni(II) were extracted from chloride solutions in a hollow-fiber module to a kerosene solution of Aliquat 336, and the extracted Co(II) and Ni(II) were then stripped by HCl solution in another module. A mass-transfer model that takes into account aqueous-layer diffusion, membrane diffusion, and organic-layer diffusion was applied to fit the time changes of the concentration of Co(II) in the aqueous phase. Chemical reactions occurring at the organic-aqueous interface were assumed to attain equilibrium instantaneously, and a simplified thermodynamic relationship that considers nonideality in the organic phase was proposed on the basis of batch solvent extraction results. Under the ranges tested, it was found that the mass-transfer coefficients of the complex and amine in the membrane phases in the stripping module were about 50 times smaller than those obtained in the extraction module. In this situation, the calculations agreed well with the measured results. Improvement of the mass transfer in the stripping module was needed and obtained through the use of hydrophilic fibers or hydrophobic fibers with a small wall thickness or larger pore size.