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Ferromagnet/Semiconductor heterostructures have attracted much attention because of their potential applications in spintronic devices. We investigated the electronic structures and magnetism of monolayer Fe on CuGaSe2(001) by using the all-electron full-potential linearized augmented plane-wave method within a generalized gradient approximation. We considered the monolayer Fe deposited on both the CuGa atoms terminated (CuGa-Term) and the Se atom terminated (Se-Term) surfaces of CuGaSe2(001). The calculated magnetic moment of the Fe atom on the CuGa-Term was about 2.90 mB. Those of the Fe atoms on the Se-Term were in the range of 2.85-2.98 mB. The different magnetic behaviors of the Fe atoms on two different surfaces were discussed using the calculated layer-projected density of states.