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Black phosphorus (BP) is a new two-dimensional (2D) material. It has received significant attention because of its great potential in the field of optoelectronics, which arises due to its low-dimensional effects. In this paper, the effect of bi-axial strain on the band structure of monolayer BP has been studied by using the first-principles method based on density functional theory (DFT). We find that the band gap range of monolayer BP can be moderately and effectively adjusted by external stress from 0 to 1.845 eV. Simultaneously, the direct band gap is maintained during the stretching process, which leads to a high electron mobility suitable for applications. Moreover, the compressive strain can result in a semiconductor–metal transition (SMT) with few-layer BP, whereas tensile strain only affects the band gap. Based on the electronic properties of monolayer BP, its optical properties are analyzed in detail, and the influence of strain—from a compressive strain of 12% to a tensile strain of 12%—on these properties is systematically discussed. It is found that the strain range and mode have a significant impact on the optical properties. In addition, the dielectric function and absorption spectra calculated along two different directions indicate that a significant optical anisotropy appears, giving a strong directionality dependence in the primitive and strained monolayer BP. It can be concluded that by applying external stress to monolayer BP, its optical properties can be readily controlled, which is beneficial for device applications. Furthermore, based on its direction-dependent response to the external stress, this behavior can also be used to detect the orientation of the deposited BP without the need for precise electron microscopy. [ABSTRACT FROM AUTHOR]