Two-dimensional materials open up tremendous opportunities for nanoelectronics and optoelectronics. Using first-principles density functional methods, we predict a family of two-dimensional boron-pnictogen materials. Our results show that these materials have excellent energetic, dynamical, thermal, mechanical, and chemical stabilities. The intrinsic structural anisotropy found in these materials leads to highly direction-dependent mechanical, electronic, and optical properties. They possess highly anisotropic Young's modulus and Poisson's ratio. The tensile strength under uniaxial and biaxial deformations is found to be very high for these materials. Electronically, they are all semiconductors with narrow band gaps. The band gap energies can be tuned by alloying, strain engineering, and chemical functionalization. They exhibit anisotropic and high carrier mobility. All these electronic properties make them promising candidates for nanoelectronic device applications. Using state-of-the-art GW- Bethe-Salpeter equation approach, taking the electron-hole effect into account, the prominent optical absorption structure with strong anisotropy in the visible light region endow the boron-pnictogen materials with great potential in optoelectronics.