In this study, growth of Au-free InAs/InSb vertical heterostructure (HS) nanowires (NWs) on highly lattice mismatched Si (1 1 1) substrate by metal organic chemical vapor deposition (MOCVD) is demonstrated. Careful selections of InSb growth parameters lead to In-rich growth regime such that direct impingement of growth precursors on top of grown InAs NW (self-assembled) stems result in axial InSb HSs nucleation on InAs stems. The observed indium (In) droplet on InSb HS NW tip shows that InSb HS growth followed a self-catalyzed growth mechanism. InSb HS axial growth rate and morphology are controlled by growth temperature and growth time. A small change in the growth parameters significantly affects In particle accumulation, particle size and its chemical composition, and thus affects the InSb nucleation on the stem. Especially, it is found that (i) growth time of less 10 min yields vertical InSb HS NW on the top of the InAs stem, (ii) as the growth time increases above 10 min, the growth turned to be InSb wrapped InAs/InSb core-shell HS due to coaxial lateral growth. High resolution transmission electron microscopy (HRTEM) study reveals that all the InSb HSs exhibit pure zinc-blende (ZB) crystal structure. The results presented here provide significant guidelines for external catalyst-free InAs/InSb HS NW growth using MOCVD on silicon (Si) substrate for various optoelectronics and electronics applications.