Abstract We have investigated the electronic properties of heterostructures MoS2-ReS2 and ReS2-MoS2 with hybrid density functional theory. Contrary to the reported work, we found that ReS2 is an indirect band gap semiconductor material in the 2H phase, in good agreement with experimental work. Furthermore, the calculated charge density profile and weighted bands show that MoS2-ReS2 heterostructures have type-II band alignment whereas ReS2-MoS2 have type-I band alignment with indirect band gaps, which are in good agreement with the literature. In MoS2-ReS2 heterostructures, both electrons and holes were positioned in ReS2 layer in the form of an exciton, while in ReS2-MoS2 the electrons and holes were located in different layers which separated the electrons and holes into two different regions. The former heterostructure material is useful to the photovoltaic devices and the later is for the application of optoelectronic devices.