We have performed magnetoresistance (MR) measurements for a BaIrO3 single crystal. As the magnetic field changes from 0 T to 14 T and back to 0 T, the longitudinal MR at 1.5 K traces out a butterfly-shaped hysteresis curve and the sign of the MR ratio for the field-ascending sweep changes from negative to positive near 6 T. The MR ratios for field-ascending and descending sweeps overlap each other around 13 T. A large anisotropic magnetoresistance (AMR) ratio per mu B, (rho parallel to - rho perpendicular to) rho(0) similar to 400 %/mu B at 1.5 K, is obtained, where rho parallel to, rho perpendicular to, and rho(0) are the longitudinal resistivity, the transverse resistivity, and the zero- field resistivity. The MR effects are interpreted based on a spin valve model considering a novel crystal structure and a local magnetic-anisotropy related to the spin-orbit coupling of this compound.