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.