Cadmium selenide (CdSe) nanocrystals are important photoelectric materials. Doping heterovalent impurities such as silver (Ag) in CdSe nanocrystal quantum dots (QDs) can provide additional charge carriers, which can significantly enhance the performance of CdSe QDs for their potential applications in high-efficiency photovoltaic devices. Using density functional theory (DFT) based calculations with the Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functional, we demonstrate that Ag doping can affect the structural, electronic and optical properties of CdSe QDs significantly. The location and number of Ag dopant atoms are critical factors for modifying the electronic structure, in particular the change of energy position and shape of the valence and conduction band edges. It is found that doping of Ag atoms into the core region of a CdSe nanoparticle induces metallic-like electronic characteristics with a dense number of electrons emerging at the Fermi level. However, incorporation of Ag dopant into the surface of a CdSe quantum dot introduces some mid-gap states that mainly consist of Se 4p states, and results in a new sub-bandgap electronic transition from mid-gap states to the conduction band. The calculated absorption spectra indicate that doping of just one or two Ag atoms greatly strengthens the absorption in the ultraviolet-visible regime and extends the absorption edges of CdSe QDs into the infrared regime. In particular, the spectra show a high-intensity absorption band between 424 and 600 nm with just 1 Ag atom incorporated into the CdSe QDs. Based on the improved absorption spectra, the present results provide a science-based strategy for designing Ag-doped CdSe QDs with enhanced visible light absorption for their application in high-efficiency photovoltaic devices.