Surface reconstructions of InSb(001) during molecular beam epitaxy are studied using reflection high energy electron diffraction (RHEED). We observe several previously unreported reconstruction regimes; namely 3D(1 1), co-existence of (4 2) with c(8 2), and co-existence of Sb-terminated and In-terminated structures. It is postulated that the only intrinsic structures in the growing InSb(001) surface are the (2 4)/c(2 8) Sb-dimers-terminated and the corresponding (4 2)/ c(8 2) In-dimers-terminated structures. The pseudo-(1 3) pattern is believed to result from a mixture of different (2 4) phases, rather than a single surface structure. The narrow transition region between In-rich and Sb-rich growth exhibits RHEED patterns which are temperature dependent. These patterns represent surfaces that contain mixtures of Sb-terminated and In-terminated structures.