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 $CuGaSe_2(001)$ 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 $CuGaSe_2(001)$. The calculated magnetic moment of the Fe atom on the CuGa-Term was about $2.90;{{mu}_B}$. Those of the Fe atoms on the Se-Term were in the range of $2.85-2.98;{{mu}_B}$. The different magnetic behaviors of the Fe atoms on two different surfaces were discussed using the calculated layer-projected density of states.