In virtue of first principle calculations based on density functional theory, we have investigated the magnetism of transition metal triiodides XI3 (X = Cr, Mn, Fe, Mo, Tc, Ru, W, Re, Os) monolayers. Our results indicate that CrI3, TcI3, RuI3, ReI3 and OsI3 monolayers are ferromagnetic (FM), while MnI3, FeI3, MoI3 and WI3 monolayers are antiferromagnetic (AFM). Interestingly, TcI3, RuI3, ReI3 and OsI3 monolayers have considerable magnetic anisotropy energy (MAE). Especially, ReI3 monolayer exhibits the largest MAE (-36.22 meV/ReI3) in known two-dimensional (2D) van der Waals (vdW) crystals. We further demonstrate that biaxial strain can greatly change MAEs of ReI3 and OsI3 monolayers. From the electronic structure analysis, the change in MAE is mainly attributed from the charge transfer between the a and e 2 states induced by biaxial strain. In addition, we have also found that a tensile strain can lead to a phase transition of ReI3 from FM to AFM. We predicted that 2D FM XI3 monolayers are promising candidates for the application in tunable magnetic storage technology.