The surface structure of 0.8 monolayers (ML) Ga on an Si (001) 2X1 surface has been studied with scanning tunneling microscopy (STM). Periodical clusters, aligned in [110] directions on an Si (001) surface and reflecting the polarity of terraces on that surface, were observed. The clusters of Ga consist of the 8X5 phase. From the line profiles of the clusters in STM images, each cluster of the 8X5 phase has been found to consist of Ga double layers, the top layer of Ga being composed of four Ga atoms. Clusters in contiguous arrays are out of phase in the direction of the arrays. Pairs of two Ga atoms exist in both longitudinal sides at each cluster along the contiguous arrays. These pairs of two Ga atoms at both sides of the valleys between the contiguous arrays are located alternatively. From the above information on positions of Ga atoms, arrangements of Ga atoms of the clusters of the 8X5 phase are presumed. Two cases are considered for the arrangements of the clusters based on the arrangements of Si atoms on the top and second layers of Si (001). It is concluded that the lateral direction of clusters is parallel to the rows of the top and second layers of Si (001).