The magnetism and electronic structure of bcc $Al_1Fe_{26}$ was investigated by means of first-principles calculations with and without spin-orbit coupling (SOC). From the calculated total energy, the SOC corrected system is shown to be approximately 5 meV per atom lower than the SOC uncorrected system. The induced spin magnetic moment at the Al site was -0.125 ${mu}_B$ without SOC and -0.124 ${mu}_B$ with SOC. The orbital magnetic moments were calculated to be 0.002 ${mu}_B$ in [$overline{1}$00] direction for Al. The electronic structures showed the nearest neighbor antiferromagnetic interaction between Fe and Al to be essential for determining the magnetism of the $Al_1Fe_{26}$ system.