Based on results of density functional theory (DFT) calculations with the local spin density approximation (LSDA) and the generalized gradient approximation (GGA), we propose a new magnetic material, CsCl-type FeSe. The calculations reveal the existence of ferromagnetic (FM) and antiferromagnetic (AFM) states over a wide range of lattice constants. At 3.12Å in the GGA, the equilibrium state is found to be AFM with a local Fe magnetic moment of ±2.69 µ B . A metastable FM state with Fe and Se local magnetic moments of 2.00 µ B and −0.032 µ B , respectively, lies 171.7 meV above the AFM state. Its equilibrium lattice constant is ∼ 2 % smaller than that of the AFM state, implying that when the system undergoes a phase transition from the AFM state to the FM one, the transition is accompanied by volume contraction. Such an AFM-FM transition is attributed to spin-density z-reflection symmetry; the symmetry driven AFM-FM transition is not altered by spin-orbit coupling. The relative stability of different magnetic phases is discussed in terms of the local density of states. We find that CsCl-type FeSe is mechanically stable, but the magnetic states are expected to be brittle.