Despite numerous studies, coupled spin and valley physics is currently limited to two-dimensional (2D) transition-metal dichalcogenides (TMDCs). Here, we predict an exceptional 2D valleytronic material associated with the spin-valley coupling phenomena beyond 2D TMDCs - single-layer (SL) H-Tl2O. It displays large valley spin splitting (VSS), significantly larger than that of 2D TMDCs, and a finite band gap, which are both critically attractive for the integration of valleytronics and spintronics. More importantly, in sharp contrast to all the experimentally confirmed 2D valleytronic materials, where the strong valence-band VSS (0.15-0.46 eV) supports the spin-valley coupling, the VSS in SL H-Tl2O is pronounced in its conduction band (0.61 eV), but negligibly small in its valence band (21 meV), thus opening a way for manipulating the coupled spin and valley physics. Moreover, SL H-Tl2O possesses extremely high carrier mobility, as large as 9.8×103cm2V-1s-1.