Resistance-temperature (R-T) characteristics were measured directly at single-grain boundaries in 0.1-mol%-niobium-doped barium titanate bicrystals that had been fabricated from polycrystalline sinters, to determine a geometrical grain-boundary character dependence of the positive temperature coefficient of resistivity (PTCR) effect, Both random boundaries and low-Sigma boundaries exhibit a similar grain-boundary character dependence of the PTCR effect through a simple geometrical analysis, using the coincidence of reciprocal lattice points. Differences of the R-T characteristics in individual boundaries have been explained in terms of the formation of a potential barrier that is associated with the oxidation of grain boundaries during cooling, after sintering or annealing. The grain-boundary character is likely to affect the diffusivity of O2- ions and, hence, is crucial to the formation of the potential barrier.