The molecular beam epitaxial growth of GaAs on the GaAs(001)-(2 x 4) surface is investigated using a kinetic Monte Carlo-based method. The developed algorithm permits to focus on the kinetic effects in a wide range of growth conditions and enables considerable computational speedup. The simulation results show that the growth rate has a dramatic influence upon both the island morphology and Ga surface diffusion length. The average island size reduces with increasing growth rate while the island density increases with increasing growth rate as well as As-4/Ga beam equivalent pressure ratio. As the growth rate increases, the island density becomes weaker dependent upon the As-4/Ga pressure ratio and approaches to a saturation value. We also discuss three characteristics of Ga surface diffusion, namely a diffusion length of a Ga adatom deposited first, an average diffusion length, and an island spacing as an average distance between islands. The calculations show that the As-4/Ga pressure ratio dependences of these characteristics obey the same law, but with different coefficients. An increase of the As-4/Ga pressure ratio leads to a decrease in both the diffusion length and island spacing. However, its influence becomes stronger with increasing growth rate for the first Ga adatom diffusion length and weaker for the average diffusion length and for the island spacing. (C) 2016 Elsevier B.V. All rights reserved.