Anatase titanium dioxide (TiO ₂) has attracted much attention due to its excellent photocatalytic properties. However, the band gap of anatase TiO ₂is 3.2 eV, which can absorb only about 4% of the ultraviolet light ( λ< 400 nm). Molybdenum disulfide (MoS ₂) is a new layered two-dimensional compound semiconductor, and it has been widely studied for its preferably optical absorption and photocatalytic properties. Moreover, the high recombination rate of photoexcited electron-hole of monolayer MoS ₂leads to low photocatalytic efficiency. In this work, based on Heyd-Scuseria-Ernzerhof (HSE06) hybrid density functional theory, the geometric structure, electronic structure, optical properties, charge transfer and effect of pressure on structure of Cu/N doped TiO ₂/MoS ₂heterostructures are systematically studied. The interface interaction between anatase TiO ₂(101) surface and monolayer MoS ₂shows that TiO ₂and MoS ₂form a van der Waals heterostructure. The defect formation energy is calculated to demonstrate that Cu@O&N@O is the most stable codoping site. The result of the density of states shows that the band gap of TiO ₂/MoS ₂heterojunction is 1.38 eV, which is obviously smaller than that of the pure anatase TiO ₂(101) surface (2.90 eV). The band gap of Cu/N doped TiO ₂/MoS ₂heterojunction obviously decreases, and an impurity band provided by Cu 3d orbitals appears in the forbidden band, which leads to the decrease of the photon excitation energy and the enhancement of the optical absorption capacity. The x-yplanar averaged and three-dimensional charge density difference of Cu/N doped TiO ₂/MoS ₂are also calculated. It is found that there are electrons' and holes' accumulation in the doped anatase TiO ₂(101) surface and the single layer MoS ₂, showing that the Cu/N doping can effectively reduce the recombination of the photoexcited electron hole pairs. Calculated optical absorption spectra show that Cu/N doped TiO ₂/MoS ₂system has obvious improvement in the absorption of visible light. In addition, we calculate the geometrical, electronic and optical absorption spectra of TiO ₂/MoS ₂heterojunction under different pressures. The results show that the appropriate increase of pressure can effectively improve the optical absorption properties of heterojunction and Cu/N doped TiO ₂/MoS ₂heterojunction and TiO ₂/MoS ₂heterojunction can effectively improve the optical properties of the material. These findings are helpful in understanding the photocatalytic mechanism and relevant experimental observations.