The structures of In-doped perovskites BaB1-xInxO3, 0 less than or equal to x less than or equal to 0.5, have been investigated by powder X-ray and neutron diffraction. Two phase transitions were observed. As the In concentration is increased, the parent monoclinic BaBiO3 first loses the breathing-mode distortions (x approximate to 0.1) and then changes the direction of octahedral tilts (x approximate to 0.4), resulting in the orthorhombic (Ibmm) and tetragonal (I4/mcm) symmetry, respectively, with random arrangement of Bi(III) and Bi(V) ions. The transport measurements show an increase of conductivity with increasing indium concentration, but the system remains semiconducting.