The initial spontaneous magnetic domains in nanoscale Fe islands on W(110) substrates are studied numerically with micromagnetic simulations. The critical anisotropies separating different domain states for irregular, elliptic and rectangular shape islands are determined precisely. A full phase diagram of magnetic domain states as a function of anisotropy and thickness is obtained, in which there is a wide transition zone separating two domain states from vortex or diamond domains, and the boundaries on two sides of the transition zone are indefinite. The calculated results indicate that the initial spontaneous magnetic domains are determined mainly by anisotropies and thicknesses, and rim shapes have significant influences on vortex and diamond domain configurations. Further study is needed to determine the exact anisotropies of nanoscale Fe islands.