Self-aligned InAs quantum wires (QWRs) or three-dimensional (3-D) islands are fabricated on GaAs(331)A substrates by molecular beam epitaxy (MBE). InAs QWRs are selectively grown on the step edges formed by GaAs layers. The surface morphology of InAs nanostructures is carefully investigated by atomic force microscopy (AFM) measurements. Different growth conditions, such as substrate temperature, growth approach and InAs coverage, exert a great effect on the morphology of InAs islands. Low substrate temperatures prefer to the formation of wire like nanostructures while high substrate temperatures favor for 3-D islands. The shape transition is attributed to the tradeoff between surface energy and strain energy.