A molecular dynamics (MD) approach which determines automatically the complex magnetic structures in itinerant electron systems is applied to Fe-Cr alloys with use of 250 atoms in a MD unit cell (5×5×5 bcc lattice). It is demonstrated that the Fe-Cr alloys show various complex magnetic structures due to competing interactions: the collinear ferromagnetism (F) of matrix Fe with antiparallel Cr moments beyond 80 at.% Fe, the coexistence of non-collinear structure of Cr and collinear F of Fe between 50 and 75 (...) at.% Fe, the coexistence of broken antiferromagnetism (AF) of Cr and the F of Fe between 25 and 45 at.% Fe, the coexistence of F of Fe and antiferromagnetic long-range order of Cr around 20 at.% Fe, the AF of Cr matrix with non-collinear Fe moments (spin-glass like structure) between 5 and 15 at.% Fe, and the AF below 5 at.% Fe. In the concentration region between 5 and 20 at.% Fe, ferromagnetic Fe pairs which are stabilized with different amplitudes of local moments are found. The magnetic phase diagram and calculated magnetic moments are shown to be consistent with the neutron, Mössbauer, and photoemission experiments. (shrink)