Two groups of heteroleptic Cu(I)-based dyes were designed and theoretically investigated by density functional theory (DFT) and time-dependent DFT (TD-DFT) methods. Different anchors were integrated into the dye skeleton to shed light on how the type of anchor influenced the electronic structure, absorption spectrum, electron excitation, and intramolecular and interfacial electron transfer of dyes. The results indicated that, compared with other dyes, the dyes with cyanoacrylic acid and nitric acid exhibited more appropriate electron distributions in frontier molecular orbitals (FMOs), lower HOMO (the highest occupied molecular orbital) –LUMO (the lowest unoccupied molecular orbital) energy gaps, broader absorption spectral ranges as well as improved spectral characteristics in the near-infrared region and better intramolecular electron transfer (IET) characteristics with more electrons transferred to longer distances, but smaller orbital overlap. Among all the studied Cu(I)-based dyes, B1 and P1 (with cyanoacrylic acid anchoring group) exhibited the best interface electronic structure parameters with a relatively short electron injection time (τinj) and large dipole moment (μnormal), which would have a positive effect on the open-circuit photovoltage (Voc) and short-circuit current density (Jsc), resulting in high power conversion efficiency (PCE) of dye-sensitized solar cells (DSSCs). Our findings are expected to provide a new insight into the designing and screening of high-performance dyes for DSSCs.