We fabricated a van der Waals heterostructure by stacking together monolayers of MoS2 and ReSe2. Transient absorption measurements were performed to study the dynamics of charge transfer, indirect exciton formation, and indirect exciton recombination. The results show that the heterostructure form a type-II band alignment with the conduction band minimum and valance band maximum located in the MoS2 and ReSe2 layers, respectively. By using different pump-probe configurations, we found that electrons could efficiently transfer from ReSe2 to MoS2 and holes along the opposite direction. Once transferred, the electrons and holes form spatially indirect excitons, which have longer recombination lifetimes than excitons in individual monolayers. These results provide useful information for developing van der Waals heterostructure involving ReSe2 for novel electronic and optoelectronic applications.