The growth processes and structures of Ga layers formed on a Si(001) surface have been studied by scanning tunneling microscopy (STM) and ab initio calculation. The 4×2-Ga structure and the precursor states of the Ga clusters that compose the Si(001) 8×n-Ga (n = 4∼6) structures are observed in addition to the 2×2-Ga structure at a Ga coverage of 0.55 ML at 300^oC. We performed an ab initio calculation of the energetics for several possible models for the 4×2-Ga structure, and clarified that the three-orthogonal-Ga-dimer model is the most stable. Also, we compare the observed STM images with the simulated ones to identify the possible structural models of the 4×2-Ga structure and the precursor state of the Ga clusters.