Constructing van der Waals heterostructures (vdWHs) has emerged as an attractive strategy to combine and enhance the optoelectronic properties of stacked materials. Herein, by means of first-principles calculations, we investigate the geometric and electronic structures of the AlP3/Cs3Bi2I6Cl3 vdWH as well as its tunable band structure via an external electric field. The AlP3/Cs3Bi2I6Cl3 vdWH is structurally and thermodynamically stable due to the low binding energy and the small energy fluctuation at room temperature. Our band structure calculations demonstrate that the AlP3/Cs3Bi2I6Cl3 vdWH possesses an indirect bandgap and a type-I band alignment with the band edges both dominated by an AlP3 layer. Notably, the band alignment of heterostructures can be flexibly tuned between type-I and type-II by employing an external electric field. Besides, an indirect-to-direct bandgap transition can be observed by increasing the intensity of negative electric field. These results reveal the potential of the AlP3/Cs3Bi2I6Cl3 vdWH as a novel candidate material for the experimental designs of multi-functional devices.