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Identifying new magnetic materials is key to better device performance and new device paradigm. Recently, the discoveries of two-dimensional (2D) ferromagnetic (FM) insulators have drawn a lot of attention to the searching of 2D magnetic materials. Here, by density functional theory calculation with different functionals as well as effective Hubbard U parameters, we symmetrically studied layered metallic magnet Fe₃GeTe₂ (FGT) from bulk to monolayer. Generally, LDA functional can give a correct description of the interlayer FM coupling, which is consistent with our experimental results. We simulated the ionic gate by electron doping in tri-layer FGT, explaining the mechanism of T_c dispersion as a function of doping level revealed in experiments, by applying Stoner model. Moreover, by obtaining the intralayer and interlayer exchange parameters, we found that the itinerant ferromagnetism persists in FGT down to monolayer with an out-of-plane magnetocrystalline anisotropy. Finally, the calculated T_c by mean field calculation is consistent with the experimental value.