We conducted Monte Carlo simulation for a Li system adsorbed on a Cu(001) surface at various coverage of adatoms, σ >1/2, σ = 1/2 and σ < 1/2. We show phase diagrams of adatom arrangements, where the axes of the diagrams are the coverage σ, strength of substrate potential λ and temperature T. First, we study the case in which the natural distance between adatoms is rather short, b_nat< √2a, where a is the unit length of the substrate lattice. Then we found atoms having a "ladder structure", which fills a surface completely at σ = 3/5, as experimental results showed. At σ = 1/2, a c(2 × 2) structure is observed; the structural factor of this arrangement shows four (± 1/2, ± 1/2) spots in diffraction space. At σ < 1/2, we observed a complex structure including several ladder structures. The structural factor of this arrangement reproduces arced streaks connecting the four spots, as have been already observed more clearly by LEED. Second, in the case in which the natural distance between adatoms is larger, b_nat ≥ √2a, the ladder structure does not appear at either σ > 1/2 or σ < 1/2. Streaks appear; however, they are not arced but straight lines forming a square shape. [DOI: 10.1380/ejssnt.2005.492]