The structural and electronic properties of two-dimensional (2D) MoS2/TiO2 heterostructure with a special configuration of Moire pattern have been investigated for the first time using first-principles methods with van der Waals correction. It is found that the new van der Waals heterostructure is of a type-II band alignment between the MoS2 and TiO2 layers, and the electronic structures of monolayer MoS2 and 2D TiO2 are well retained in their respective layers due to a weak interlayer coupling, which suggests that the heterostructure may have potential applications in many fields such as photoelectric devices, photo catalysis, energy conversion and storage, etc. Meanwhile, the heterostructure can also provide an ideal platform of two-dimensional electron gas (2DEG) and two-dimensional hole gas (2DHG) for fundamental research such as spin Hall effect, etc. In addition, it is discovered that the corresponding MoS2/TiO2 superlattice also has similar electronic properties to MoS2/TiO2 bilayer heterostructure. Furthermore, two novel design schemes based on the MoS2/TiO2 heterostructure and superlattice are proposed for a solar cell and photocatalyst, respectively. (C) 2017 Elsevier B.V. All rights reserved.