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Density-functional calculations were carried out for the (113)[−110] tilt grain boundary in the anatase modification of TiO2, with and without magnetic Co dopants. The boundary exhibits a low energy of 0.88 J/m2 and no rigid translation of the grains. It is composed from four distinct structural units, and a deviation from the mirror-symmetric atom arrangement due to local relaxation is found. The analysis of the electronic structure indicates that the grain boundary is electronically inactive, because it introduces no boundary-specific states in the bulk band gap, and only minor differences between the valence band structures of the grain boundary and the pure bulk are obtained. The regular arrangement of the quite open structural units provides the possibility of doping the grain boundary with electronically or magnetically active elements, which is explored by doping the supercell with Co. In this diluted magnetic semiconductor, the (113)[−110] grain boundary can enhance the ferromagnetic interaction by providing convenient bond angles for ferromagnetic superexchange.