Soft x-ray absorption spectra and their x-ray magnetic circular dichroism (XMCD) have been theoretically studied at the transition-metal L_2,3 thresholds of the Heusler-type Fe_2−xV_1+xAl. The electronic structure of Fe_2−xV_1+xAl upon changing the content x was theoretically investigated from first principles by using the fully relativistic Dirac linear-muffin-tin-orbital band structure method and the scalar relativistic Korringa-Kohn-Rostoker method within the coherent potential approximation generalized to treat disorder in multicomponent complex alloys. Densities of valence states and spin and orbital magnetic moments are analyzed and discussed. The origin of the XMCD spectra in the Fe_2−xV_1+xAl compound is examined. The calculated results are compared to the experimental data.