The band structure, density of states, optical properties, carrier mobility, and loss function of graphene, black phosphorus (BP), and molybdenum disulfide (MoS₂) were investigated by the first-principles method with the generalized-gradient approximation. The graphene was a zero-band-gap semiconductor. The band gaps of BP and MoS₂ were strongly dependent on the number of layers. The relationships between layers and band gap were built to predict the band gap of few-layer BP and MoS₂. The absorption showed an explicit anisotropy for light polarized in (1 0 0) and (0 0 1) directions of graphene, BP, and MoS₂. This behavior may be readily detected in spectroscopic measurements and exploited for optoelectronic applications. Moreover, graphene (5.27 × 10⁴ cm²·V^-1·s^-1), BP (1.5 × 10⁴cm²·V^-1·s^-1), and MoS₂ (2.57×10² cm²·V^-1·s^-1) have high carrier mobility. These results show that graphene, BP, and MoS₂ are promising candidates for future electronic applications.