We report molecular beam epitaxial growth of InAs on GaP(001), which has the largest lattice mismatch (11%) among all the arsenides and phosphides. Reflection high‐energy electron diffraction and high‐resolution transmission electron microscopy were used to optimize the growth and characterize the epilayer. It is found that the growth mode can be controlled by the surface V/III ratio: three‐dimensional and two‐dimensional layer‐by‐layer growths under As‐stable and In‐stable conditions, respectively. In both cases, a regular network of pure edge‐type (90°) misfit dislocations with a spacing of 4 nm was formed directly at the heterointerface, which corresponds to 85% of degree of strain relaxation. The epilayers grown under In‐stable conditions have relatively smooth surfaces with low threading dislocation densities. This is owing to the fact that the interface misfit dislocations were exclusively of the edge‐type which have no threading component and which relieve strain most effectively. The results demonstrate the ability to control the growth mode as well as the misfit dislocation nucleation type. ©1996 American Institute of Physics.