The structural, electronic, magnetic, and optical properties of Au, Cu, Cr, Mn, Co, Ni, and Fe atoms doped 13-atom silver clusters were investigated by the density functional theory (DFT) in the theoretical frame of the generalized gradient approximation (GGA) exchange-collection function. The results show that all the ground state structures of Au, Cu, Cr, Mn, Co, Ni, and Fe atoms doped 13-atom silver clusters are icosahedral, respectively. The Au atom doped on the surface of Ag13 cluster is stable, while other atoms doped in the center of Ag13 cluster are stable. The electronic stability order from high to small is Ag12Cr1, Ag12Cu1, Ag12Co1, Ag12Fe1, Ag12Au1, Ag12Mn1, Ag12Ni1. Their magnetic moments are not only related to the doping atom but also the doping location of the atom. The magnetic moments of the Cu, Au, Mn, Co, Ni, Fe, and Cr atoms doped in the Ag13 cluster are 5.0, 3.0, 1.0, 3.0, 4.0, 2.0, and 0.0μB, respectively. Compared with the optical absorption spectrum of the Ag13 cluster, the Au, Cr, and Mn atoms doped the Ag13 cluster leading to blue shift, and the Cu, Co, Ni, and Fe atoms doped the Ag13 cluster resulting in red shift. These studies provide a theoretical basis on applications for clusters in electronic, magnetic, and optical devices.