Strained InAs nanostructures have been grown by solid-source molecular beam epitaxy in In0.52Al0.48As matrix on different InP substrate surfaces ((0 0 1) and (1 1 n)A/B (n = 1 - 5)). The morphology of the nanostructures was characterized using atomic force microscopy (AFM). The AFM results reveal interesting differences in the size, shape, and alignment of the nanostructures between different oriented surfaces. It was found that some faceted nanostructures tend to form on A-type surfaces, the shape and the alignment of these nanostructures show clear dependence on the substrate orientation. Samples grown on (0 0 1) and B-type surfaces showed preferentially dense round dots. Dots formed on (1 1 3)B, (1 1 3)B and (1 1 5)B surfaces have a higher dot density and size homogeneity, which shows a potential for the production of high-quality and customized self-assembled quantum dots for photonics applications.