Two-dimensional (2D) materials with a moderate bandgap and high carrier mobility are useful for applications in optoelectronics. In this work, we present a systematic investigation of the mechanical, electronic and optical properties of a B2P6 monolayer using first-principles calculations. Monolayer B2P6 was estimated to be an anisotropic material from direction-dependent in-plane Young's moduli and Poisson's ratios. Also, B2P6 exhibits an ultrahigh electron mobility of ∼5888 cm2 V-1 s-1, showing advantages for application in high-speed optoelectronic devices. More importantly, for the B2P6 monolayer, a desirable transformation from an indirect to direct band gap was observed at a biaxial tensile strain of ∼4%. Increasing the biaxial strain reduces the gap and preserves the suitable band edge positions for photocatalytic water splitting in the observed strain range of 1-8%. The decreased gap also enhances the visible light absorption of the B2P6 monolayer. These findings indicate that the B2P6 monolayer has promising applications in photocatalytic and photovoltaic devices.