It is known that the Fe-Al transition metal compounds have a lot of disagreement about structural stability and magnetism. In this study, the correlation between magnetism and atomic structure of ordered $B_2$, $L1_2$, and $D0_3$ structured Fe-Al compounds has been investigated using the all-electron full-potential linearized augmented plane wave (FLAPW) method based on the generalized gradient approximation (GGA). We found that considered all the structures were calculated to be stabilized in a ferromagnetic state. The calculated spin magnetic moments of the Fe atoms for B2 and $L1_2$ structures were 0.771 and 2.373 ${mu}_B$, respectively, and that of Fe(I) and Fe(II) in $D0_3$ structure calculated to be 2.409 ${mu}_B$, 1.911 ${mu}_B$, respectively. In order to investigate structural stability between $L1_2$ and $D0_3$ structures, we performed the formation enthalpy calculations. As a result, the $D0_3$ structure is found to be more favorable than $L1_2 one by energy difference 16 meV/atom, which is well consistent with the experimental observation. We understood about structural stability and magnetism for Fe-Al compounds in terms of analysis of their atomic and electronic structures.