The electronic and optoelectronic properties of two-dimensional materials have been extensively explored in graphene and layered transition metal dichalcogenides (TMDs). Spintronics in these two-dimensional materials could provide novel opportunities for future electronics, for example, efficient generation of spin current, which should enable the efficient manipulation of magnetic elements. So far, the quantitative determination of charge current-induced spin current and spin-orbit torques (SOTs) on the magnetic layer adjacent to two-dimensional materials is still lacking. Here, we report a large SOT generated by current-induced spin accumulation through the Rashba-Edelstein effect in the composites of monolayer TMD (MoS or WSe)/CoFeB bilayer. The effective spin conductivity corresponding to the SOT turns out to be almost temperature-independent. Our results suggest that the charge-spin conversion in the chemical vapor deposition-grown large-scale monolayer TMDs could potentially lead to high energy efficiency for magnetization reversal and convenient device integration for future spintronics based on two-dimensional materials.