Bi thin films have been grown on InSb(1 1 1)A/B substrates using molecular beam epitaxy. We have observed different Bi atomic surface structures on polar InSb(1 1 1)A and B faces as well as thickness dependent surface structures on the A face. Bi deposited on InSb(111)B shows a (1 X 1) surface structure, i.e., no surface reconstruction. However, Bi on InSb(111)A shows a (2X2) structure for thicknesses less than 16 Angstrom, thereafter changing to a (1 X 1) structure. On both surfaces, Bi grows in a layer-by-layer growth mode with high crystallinity and sharp interfaces.