Using the first-principles plane-wave pseudopotential method within density functional theory, we systematically investigated the interaction of perylenediimide PDI-based dye compounds BrPDI, BrGly, and BrAsp with both unreconstructed UR and reconstructed RC anatase TiO2 001 surfaces. All dye molecules form strong chemical bonds with surface in the most favorable adsorption structures. In UR-BrGly, RC-BrGly, and RC-BrAsp cases, we have observed that highest occupied molecular orbital and lowest unoccupied molecular orbital levels of molecules appear within band gap and conduction-band region, respectively. Moreover, we have obtained a gap narrowing upon adsorption of BrPDI on the RC surface. Because of the reduction in effective band gap of surface-dye system and possibly achieving the visible-light activity, these results are valuable for photovoltaic and photocatalytic applications. We have also considered the effects of hydration of surface to the binding of BrPDI. It has been found that the binding energy drops significantly for the completely hydrated surfaces.