We design novel graphyne/blue phosphorene van der Waals (vdW) heterostructures (G/BP) under the external electric fields (E-field) and strains. It is demonstrated that the G/BP is a type-I semiconductor with a direct band gap of approximately 0.378 eV. The external E-field and strains not only have important effects on the band structure which undergoes a fascinating direct-indirect and semiconductor-metal transitions, but also influence the band alignment which experiences transition from type-I to type-II. In brief, the features of tunable bandgap and controllable band alignment endow G/BP with potential for application in future optoelectronic devices.