The evolution of the surface morphology of InAs nanostructures grown on InGaAs/InP by molecular-beam epitaxy was studied through atomic force microscopy imaging. Randomly distributed quantum dots and quantum wires were reproducibly achieved by adjusting proper growth parameters such as InAs deposition thickness, growth temperature, arsenic overpressure, and InAs growth rate. It is observed that a thick InAs layer, high growth temperature, high arsenic overpressure, and high growth rate promote the formation of quantum dots. We propose that when InAs is deposited, the interaction of the total strain in the InAs layer and the surface strain distribution in the underlying matrix layer might be the determinant factor of the nanostructure morphology. Thick InAs, which increases the total strain of the InAs layer, is preferred to form quantum dots. Surface diffusion of In adatoms is another important factor affecting the surface morphology. A high growth temperature promotes homogeneous diffusion, while a high arsenic overpressure and growth rate reduces the surface diffusion of the In adatoms. These factors induce the formation of quantum dots. © 2003 American Institute of Physics.