We report the formation mechanism and the characteristics of catalyst-free and mask-free heteroepitaxial GaN submicrometer- and micrometer-sized rods (SMRs) under biaxial strain grown on Si(111) substrates by metal-organic chemical vapor deposition. We found that the GaN SMRs on Si(111) substrates were subject to strong tensile strain on their N-terminated top (000 (1) over bar) GaN surface due to the lattice mismatch between GaN and Si. Our calculations based on the density functional theory showed that the (000 (1) over bar) GaN surface energy increased (decreased) monotonically with increasing tensile (compressive) strain, resulting in a faster GaN growth rate of the tensile-strained top (000 (1) over bar) surface of GaN SMRs than that of the compressive-strained one. We experimentally verified this result by comparing GaN on Si(111) substrates with tensile strain and on 6H-SiC substrates with compressive strain. In addition, we confirmed that the vertical growth rate of GaN SMRs could be controlled by adjusting growth conditions, especially the reactor pressures at low V/III molar ratio. We explained the changes in the growth rate by introducing the pressure dependency of the reaction rate constant, the chemical potential, and the surface diffusion length of Ga adatom on the surface of the SMRs.