Förster resonance energy transfer (FRET) using colloidal semiconductor quantum dots (QDs) and dyes is of importance in a wide range of biological and biophysical studies. Here, we report a study on FRET between CuInS2/ZnS QDs and dark quencher dye molecules (IRDye QC-1). Oleate-capped QDs with photoluminescence quantum yields (PLQYs) of 55 ± 4% are transferred into water by using two types of multifunctional polymer ligands combining imidazole groups and specific moieties with amine or methoxy groups as the terminal sites. The resulting water-dispersible QDs show PLQYs as high as 44 ± 4% and exhibit long-term colloidal stability (at least 10 months at 4 °C in the dark) with a hydrodynamic diameter of less than 20 nm. A side-by-side comparison experiment was performed using the amine or methoxy-functionalized QDs for coupling to dark quencher dye molecules. The amine-functionalized QDs bind to the dye molecules via covalent bonds, while methoxy-functionalized ones bind only weakly and nonspecifically. The progressive quenching of the QD emission and shortening of its photoluminescence decay time upon increasing the number of conjugated dye molecules demonstrate that the QD acts as the energy donor and the dark quencher dye as the energy acceptor in a donor-acceptor FRET pair. The FRET dynamics of the QD-dye conjugates are simulated using two different models based on the possible origin of the multiexponential PL decay of the QDs (i.e., variations in nonradiative or radiative decay rates). The model based on the radiative decay rates provides a better fit of our experimental data and estimates a donor-acceptor distance (6.5 nm) that matches well the hydrodynamic radius of the amine-functionalized QDs.