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Constructing van der Waals (vdW) hetero-structure by stacking different twodimensional (2D) materials has become an effective method for designing new-type and highquality electronic and optoelectronic nano-devices. In this work, we designed a 2D As/BlueP vdW hetero-structure by stacking monolayer arsenene (As) and monolayer blue phosphorous (BlueP) vertically, which were recently implemented in experiments, and investigated its structural, electronic, and photocatalytic water splitting properties by using the standard first principles calculation method with HSE06 hybrid exchange-correlation functional. Numerical results show that the As/BlueP vdW hetero-structure is structural robust, even at room temperature. It presents semi-conducting behavior, and the conduction band minimum (CBM) and the valence band maximum (VBM) are dominated by BlueP and As, respectively. The typical type-II band alignment predicts the potential application of the hetero-structure in highly efficient optoelectronics and solar energy conversion. Moreover, the CBM and the VBM straddle the redox potentials of water in acid environment, predicting the possibility of the As/BlueP hetero-structure as a 2D photocatalyst for water splitting. When an in-plane strain is applied, the band edges and, further, the optoelectronic properties of the hetero-structure can be effectively tuned. Especially, when tensile strain is equal to 4.5%, the optical absorption spectrum is effectively broadened in a visible light region, which will largely improve its photocatalytic efficiency, although the pH value of the solution range reduction. This work provides theoretical evidence that the As/BlueP hetero-structure has potential application as a 2D photocatalyst in water splitting.