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The electronic structure and band offsets of blue phosphorus/WSe₂ van der Waals (vdW) heterostructure are investigated via performing first-principles calculations. Blue phosphorus/WSe₂ vdW heterostructure exhibits modulation of bandgaps by the applied vertical compressive strain, and a large compressive strain of more than 23% leads to a semiconductor-to-metal transition. Blue phosphorus/WSe₂ vdW heterostructure is demonstrated to have a type-II band alignment, which promotes the spontaneous spatial separation of photo-excited electrons and holes. Furthermore, electrons concentrating in BlueP and holes in WSe₂ can be enhanced by applied compressive strain, resulting in an increase of carrier concentration. Therefore, these properties make blue phosphorus/WSe₂ vdW heterostructure a good candidate for future applications in photodetection.