Anatase titanium dioxide (TiO₂) has attracted much attention due to its excellent photocatalytic properties. However, the band gap of anatase TiO₂ is 3.2 eV, which can absorb only about 4% of the ultraviolet light (λ < 400 nm). Molybdenum disulfide (MoS₂) 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 MoS₂ leads 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 TiO₂/MoS₂ heterostructures are systematically studied. The interface interaction between anatase TiO₂(101) surface and monolayer MoS₂ shows that TiO₂ and MoS₂ form 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 TiO₂/MoS₂ heterojunction is 1.38 eV, which is obviously smaller than that of the pure anatase TiO₂(101) surface (2.90 eV). The band gap of Cu/N doped TiO₂/MoS₂ heterojunction 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-y planar averaged and three-dimensional charge density difference of Cu/N doped TiO₂/MoS₂ are also calculated. It is found that there are electrons' and holes' accumulation in the doped anatase TiO₂(101) surface and the single layer MoS₂, 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 TiO₂/MoS₂ system has obvious improvement in the absorption of visible light. In addition, we calculate the geometrical, electronic and optical absorption spectra of TiO₂/MoS₂ heterojunction 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 TiO₂/MoS₂ heterojunction and TiO₂/MoS₂ heterojunction can effectively improve the optical properties of the material. These findings are helpful in understanding the photocatalytic mechanism and relevant experimental observations.