Two-dimensional semiconducting materials with moderate band gap and high carrier mobility have a wide range of applications for electronics and optoelectronics in nanoscale. On the basis of first-principles calculations, we perform a comprehensive study on the electronics and optical properties of graphene-like boron phosphide (BP) sheets. The global structure search and first-principles based molecular dynamic simulation indicate that two-dimensional BP sheet has a graphene-like global minimum structure with high stability. BP monolayer is semiconductor with a direct band gap of 1.37 eV, which reduces with the number of layers. Moreover, the band gaps of BP sheets are insensitive to the applied uniaxial strain. The calculated mobility of electrons in BP monolayer is as high as 10 6 cm 2 /(V•s). Lastly, the MoS 2 /BP van der Waals heterobilayers are investigated for photovoltaic applications, and their power conversion efficiencies are estimated to be in the range of 17.7%−19.7%. This study implies the potential applications of graphene-like BP sheets for electronic and optoelectronic devices in nanoscale.