Solvent extraction of scandium(III) from an aqueous solution, which simulates a concentrated scandium solution generated from nickel/cobalt mixed-sulfide production process, was performed using a ternary mixed extractant system. Addition of tri-n-octylphosphine oxide and a long-chain alkyl carboxylic acid (Versatic 10) to an organophosphonic ester (PC-88A) drastically improved the separation factor of scandium over zirconium in comparison with that of a single extractant system. The optimum mixing ratio in the ternary extractant system was 10 mol% PC-88A, 60 mol% tri-n-octylphosphine oxide, and 30 mol% Versatic 10. The degree of scandium extraction was 90%, and the separation factors between scandium and other metals (i.e., Al, Fe, Ni, Cr, and Zr) were > 140 at pH 2 with the optimized ternary extractant system. The operating conditions for a countercurrent multistage extraction of scandium were investigated by McCabe–Thiele analysis. Ninety-nine percent recovery from 1800 mg dm−3 scandium was achieved by two- to three-stage countercurrent extraction at the flow ratio (A/O) = 1.01. The stripping efficiency of scandium reached >98% with 7 mol dm−3 H3PO4. Based on the results, a conceptual flowsheet for scandium recovery from waste solutions of laterite ore leachate is proposed.