Abstract: The two-dimensional (2D) transition metal trihalide (TMX3, X = Cl, Br, I) family has attracted considerable attention in recent years due to the realization of CrCl3, CrBr3, and CrI3 monolayers. Up to now, the main focus of the theoretically predicted TMX3 monolayers has been on the Chern insulator states, which can realize the quantum anomalous Hall effect. Here, using first-principles calculations, we theoretically demonstrate that the stable OsCl3 monolayer has a ferromagnetic ground state and a spin-polarized Dirac point without spin-orbit coupling (SOC), which disappears in the band structure of a Janus OsBr1.5Cl1.5 monolayer. We find that OsCl3 exhibits in-plane magnetization when SOC is included. By manipulating the magnetization direction along the C-2 symmetry axis of the OsCl3 structure, a gapless half-Dirac semimetal state with SOC can be achieved, which is different from the gapped Chern insulator state. Both semimetal states of OsCl3 monolayer without and with SOC exhibit a linear half-Dirac point (twofold degenerate) with high Fermi velocities. The achievement of the 2D semimetal state with SOC is expected to be found in other TMX3 monolayers, and we confirm it in a TiCl3 monolayer. This provides a different perspective to study the band structure with SOC of the 2D TMX3 family.