The electronic and the magnetic properties of Fe single-layered atomic shees separately with two-dimensional square and hexagonal structures are calculated by the first-principles method based on the spin-polarized density functional theory. The calculations show that planar square and hexagonal as well as the bcc structures manifest their magnetisms at their equilibrium lattice constants. The magnetic moments for these structures are 2.65, 2.54 and 2.20μВ, respectively. The calculated magnetic properties for the elongated and the compressed bond lengths suggest that when the bond is stretched to a length larger than 4.40, the bond should be broken and the magnetic moments of the systems reach the magnetic moment of an independent Fe atom, 4μВ. When the bond lengths are reduced, the magnetic moments of all the systems studied decrease correspondingly. At the critical bond lengths (1.80 for planar square lattice, and 1.75 for hexagonal lattice), the magnetisms of the two planar lattices disappear. Using the Stoner theory, the change from magnetism to non-magnetism for the lattice compression is elucidated.