Hybrid density functional has been adopted to investigate the structural, electronic, and optical properties of ZnO/MoS₂ and ZnO/MoSe₂ composites as compared with the results of ZnO, MoS₂, and MoSe₂ monolayers. The results indicate that MoS₂ and MoSe₂ monolayers could contact with monolayer ZnO to form ZnO/MoS₂ and ZnO/MoSe₂ heterostructures through van der Waals (vdW) interactions. The calculated bandgap of ZnO/MoS₂ (ZnO/MoSe₂) is narrower than that of ZnO or MoS₂ (MoSe₂) monolayers, facilitating the shift of light absorption edges of the composites towards visible light in comparison with bare ZnO and MoX₂ monolayers. Through the application of strain, the ZnO/MoS₂ and ZnO/MoSe₂ composites which own suitable bandgaps, band edge positions, efficient charge separation, and good visible light absorption will be promising for visible light photocatalytic water splitting. These results provide a route for design and development of efficient ZnO/MoS₂ and ZnO/MoSe₂ photocatalysts for water splitting.