The in-plane orientation-dependent electrical and optical properties of two-dimensional (2D) anisotropic materials attract significant attention because of the intriguing underlying physics. However, this feature limits their further development in polarization-independent applications such as refractive index sensors and light absorbers. In this paper, polarization-independent optical properties of black phosphorous (BP) metadevices are achieved by the design of a single-layer pattern of 2D anisotropic material. Finite-difference time-domain (FDTD) simulation results indicate that the absorption spectrum remains unchanged as the polarization angle of the incident light varies from 0° to 360°. The performance of the BP metadevices when used as refractive index sensors is also studied. The results show that the polarization-independent BP sensors exhibit high sensitivity and figures of merit (FOMs). This work opens up the possibility of fabricating optically polarization-independent devices based on a single-layer pattern of 2D anisotropic material.