The recovery of rare earth elements (REEs) from discharged electronic devices or mineral waste water is highly essential but still facing challenges. In this work, two amino-functionalized carboxyl-UiO-66 (UiO-66-COOH-TETA and UiO-66-(COOH)2-ED) prepared via the postmodification method were employed as the adsorbents for Yb(III) capture. The experimental results revealed their superior adsorption capacities of 161.5 and 202.6 mg/g, respectively. Meanwhile, their adsorption processes can be described by the pseudo-second-order kinetic model and Langmuir model. Effects of initial pH and temperature on adsorptions were systematically evaluated, affording an optimal operating condition (i.e., pH of 5.5-6, T of 65 °C, t of 10 h). Moreover, the fabricated materials exhibited great reusability after five adsorption-regeneration cycles. UiO-66-COOH-TETA demonstrated good separation selectivity for Yb(III) over light REEs (i.e., 3.98 of Yb/Ce, 3.51 of Yb/Nd). Based on the density functional theory calculations and characterization analysis (XPS, Zeta, mapping, and IR), the adsorption mechanisms were mainly attributed to significant electrostatic attraction and strong surface complexation between N and O sites and Yb(III).