2D ferromagnets show promising applications in low energy spintronics. However, the small magnetic anisotropy imposes a great limitation on the application scope. By using first principles modelling, we for the first-time report substantial tuning of magnetic anisotropy of a ferromagnetic CrI₃ monolayer via a molecular adsorption strategy. We find that electron or hole doping has a significant impact on the magnetic anisotropy energy of 2D CrI₃. Then we propose to realize charge carrier doping by the adsorption of electrophilic/nucleophilic molecules (TCNQ/TTF) on 2D CrI₃. The largely controllable magnetic anisotropy is confirmed due to the interfacial electrostatic effects. Additionally, the out-of-plane magnetic anisotropy is also sensitive to the concentrations of organic molecules. The highest value reaches 1.17 meV Cr⁻¹ in the hole-doped TCNQ-CrI₃, while the lowest one is 0.20 meV Cr⁻¹ in the electron-doped TTF-CrI₃. Our work offers a feasible route to modulate the magnetic anisotropy of 2D magnets for practical magnetic applications.