Here, using first-principles calculations based on density-functional theory, we propose a novel member of the two-dimensional (2D) transitional metal dichalcogenide family known as a Janus CrSSe monolayer (denoted as CrSSe-ML). The 2D CrSSe-ML has a hexagonal crystal structure. The calculated phonon band structure suggests Janus CrSSe-ML is dynamically stable, and formation energy indicates thermodynamic stability. At the equilibrium lattice constant, it is reported that 2D Janus CrSSe-ML is a non-magnetic semiconductor with a direct bandgap of 0.93 eV (K–K). We found that compressive biaxial strain induces no local magnetic moment, while in contrast the tensile biaxial strain of 12% induces a magnetic moment of 2 μB and half-metallicity which is robust up to 20%. Furthermore, we studied the ferromagnetic (FM) and antiferromagnetic (AFM) coupling between Cr atoms in CrSSe-ML and found that the FM state is favorable over AFM by the amount of energy of 0.007 meV, which is less than 0.03 eV, so no room-temperature ferromagnetism is possible. At the end, we added the H atom at the most preferable Se top-site in a Janus CrSSe-ML and found that hydrogenated Janus CrSSe-ML is magnetic and half-metallic at the equilibrium lattice constant. We further studied FM and AFM calculation by considering fully hydrogenated 4 × 4 × 1 supercell of a Janus CrSSe-ML. We used quantum Monte Carlo simulations (MC) to estimate the Curie temperature (Tc) of hydrogenated CrSSe-ML under normal conditions. The calculated value of Tc is 553.96 K using the quantum MC simulations. Our calculations predicted that the 2D Janus CrSSe-ML material is a promising candidate for spintronic device applications above room temperature.