The dependence of magnetic properties on lattice constants in both body-centered-cubic (bcc) and facecentered-cubic (fcc) FexMn1-x (x=0, 0.25,0.5,0.75,1) has been studied systematically using first-principles linearized augmented plane-wave (LAPW) calculations. The results indicate that the magnetic properties of bcc FexMn1-x alloys are ferromagnetism within a fairly large range of lattice constants, and the atomic moment increases with an increase of the lattice constants. However, for fcc FexMn1-x alloys, the magnetic properties change from paramagnetism to antiferromagnetism (or ferrimagnetism) and finally to ferromagnetism with an increase of the lattice constants. The calculated magnetic moment is consistent with previous experiments for bcc FexMn1-x alloys at the normal lattice constants, while for fcc FexMn1-x alloys on the whole the magnetic properties are also in agreement with the experimental results. The present results may facilitate a better understanding of the correlation between the structures and the corresponding magnetic properties.