The formation mechanism of one-dimensional Si islands on a H/Si(001)-(2x1) surface is studied using scanning tunneling microscopy/spectroscopy and first-principles calculations. We observed that one-dimensional islands that are made from dimer chains are formed at the initial growth stages similar to the bare Si(001) surface. It is found that the number of odd-numbered dimer chains is larger than that of even-numbered dimer chains. We propose the growth processes of the two types of growth edges to explain the observation.