Van der Waals (vdW) heterostructures, which have the advantage of integrating excellent properties of the stacked 2D materials by vdW interactions, have gained increasing attention recently. In this work, within the framework of density functional theory calculations, the electronic properties of vdW heterostructure composed of phosphorene (BP) in black phosphorus phase and GeS monolayer are systematically explored. The results show that the carriers are not separated for both lattice-match and lattice-mismatch heterostructures. For the lattice-match heterostructure, it is found that changing monolayer of GeS to bilayer can increase the energy difference of valence band offsets between GeS and BP, thus realizing electron-hole separation. For the lattice-mismatch heterostructure, altering the layer distance can transform the heterostructure into a typical type-I alignment, but applying the electric field or doping with 2, 3, 5, 6-tetrafluoro-7, 7, 8, 8-tetracyanoquinodimethane (F4TCNQ) can make it display a perfect desirable type-II alignment, where holes migration and electrons transfer are revealed to account respectively for the phenomenon of carrier separation. It is believed that the work would greatly enlarge the potential application of the BP-based heterostructures in photoelectronics and further stimulate the investigation enthusiasms on other fashionable heterostructures and even unassuming heterostructures in which the charming electronic properties can be modulated to emerge by various general methods.