The kinetic Monte Carlo method is used to study the initial stage of GaAs molecular beam epitaxial growth on the GaAs(001) surface via fluxes of Ga atoms and As tetramers. The developed algorithm allows efficient investigation of the effects of the V/III flux ratio upon the geometrical characteristics of islands in the temperature range at which the (2 × 4) reconstruction of GaAs(001) is exclusively observed. The island density increases with an increasing V/III flux ratio, whereas the average island size decreases. The temperature dependences of the island characteristics are observed to be stronger at a smaller V/III flux ratio because large arsenic fluxes compensate the enhanced desorption at high temperatures. The island size distribution is more uniform at small V/III flux ratios, while a higher concentration of small clusters is observed as the arsenic flux increases. The analysis of the island morphology and size distribution function suggests that an increase in the V/III flux ratio and a decrease in the substrate temperature have similar effects upon island characteristics, which are attributed to suppression of surface diffusion in both cases.