Based on the density functional theory, we investigate the structural, electronic, and magnetic properties of graphene sheet with substitutional Ge atoms in both single and double vacancies, and graphene sheet with Ge-chain impurity. We find the substitutional Ge is chemically bonded to graphene, and is more stable in the double vacancy site. The electronic properties indicate that metallic and semiconductor states with a range of band gaps from 0 to 0.87 eV could be obtained depending on different substitution sites, concentrations, and vacancy types. Magnetic moment is observed in graphene with single vacancy. Tunable electronic behaviors are also observed in graphene sheet with Ge-chain impurity, and a magnetic moment of 2.9 mu B is observed in single Ge-chain incorporated 4 x 4 graphene supercell. From these investigations, we conclude that by doping of Ge in vacancy-contained graphene, it could provide great advantages for its application in future nanoscale devices. (C) 2016 Elsevier B.V. All rights reserved.