Group-ⅢA metal-monochalcogenides have been extensively studied due to their unique optoelectronic and spin electronic properties. To realize the device applications, modifying their magnetic properties is desirable. Atomic doping and vacancy defects have been proven to produce itinerant ferromagnetism and half-metallicity in GaSe monolayer. Relatively, the magnetic modification by adsorbing foreign atoms is rarely reported. Traditional ferromagnetic material, Fe element, possessing high electronic polarizability and high Curie temperature, becomes the best option of adsorbate. In this work, Fen(n=1, 2) atoms adsorbed GaSe monolayer systems are constructed, and the spin electronic properties are systematically studied through the density function theory. Based on the geometric configuration of fully relaxed 33 GaSe supercell, three highly symmetrical sites, i.e., the hollow site, the top site of Se atom, and the top site of Ga atom are inspected to search for the stable absorption positions of Fen atoms. Computation results of adsorption energies indicate that the top site of Ga atom is preferred for single Fe atom, and the hollow site near the first Fe adatom is the most stable site serving as adsorbing the second Fe atom. Based on the most stable configuration, the spin electronic properties are studied. For the single Fe adsorbed system, the valence band maximum moves to point, resulting in a direct-band-gap. The strong orbit coupling effect between Fe adatom and its nearest Ga and Se atoms causes un-coincident majority and minority spin channels. Two impurity bands are located near the Fermi level and contribute only to the minority spin channel, producing a half-metallicity with a 100% spin polarization in the system. Bader charge analysis and spin-resolved partial density of states suggest that the spin polarization is mainly attributed to the transfer of Fe-3d electrons, and the hybridizations of Fe-3d, Se-4p, and Ga-4p states. Charge transfer from the Fe adatom to GaSe generates an n-type doping and an antiferromagnetic coupling between Fe and vicinal Ga and Se atoms. For the two-Fe-atoms adsorbed GaSe monolayer, the spin electronic states are found to be mainly located between the two Fe adatoms, leading to the reduction of the charge transfer from Fe to GaSe ML. As the original single spin channel turns into two spin channels (majority spin channel and minority spin channel) near the Fermi level, the ferromagnetic coupling between Fe atom and the vicinal Se atoms turn into antiferromagnetic coupling and the spin polarization falls to 0%. Therefore, the spin properties of GaSe monolayer can be controlled by modifying the number of adsorbed Fe atoms. These results reveal the formation and transform of the spin electronic properties of typical ferromagnetic/GaSe adsorption system, which offers some advice for designing and constructing the two-dimensional spin nanostructures.