Several methods have been introduced to study and simulate homoepitaxial growth of III-V materials. GaAs (001) surface has widely been used in the last three decades due both to its importance as substrate and for characterization of epitaxial growth. In this paper, we firstly study the initial stage of homoepitaxial growth on a GaAs (001) β2(2x4) reconstructed surface using As2 . The simulation was carried out with Kinetic Monte Carlo simulations including the zinc blend structure β2 (2x4) reconstruction of GaAs surface. Then we discus results of the homoepitaxy GaAs on GaAs particularly morphological evolution of the two dimensional islands and observations were made in real-time at the growth temperature using reﬂection high energy electron diffraction (RHEED) and roughness morphology.