Two-dimensional III-V binary compounds are considered as high-performance optoelectronic materials due to their tunable bandgap and unique photoelectric properties. In this research, the effects of strain engineering on the electronic properties and optical properties of hexagonal boron phosphide monolayer have been systematically studied by using first principles calculations. The bandgap is enlarged monotonously while the direct bandgap character remains as the strain increases from -10% (compression) to +10% (tension), suggesting its application prospect in flexible electronics. Interestingly, the hexagonal boron phosphide monolayer exhibits a large optical absorption coefficient in both visible and ultraviolet regions, and could reach 1.3 × 10 6 cm -1 in ultraviolet region. As compressive strain gets larger, the main peak of dielectric function as well as the edge of optical absorption appear redshift. In addition, the absorption spectrum broadens in visible light region and the light absorption intensity becomes larger in ultraviolet range with increasing compressive strain. The calculated optical properties prove that hexagonal boron phosphide monolayer is a suitable material as ultraviolet-visible dual band photodetectors and a potential auxiliary material for quantum cutting.