Single-layer black phosphorus (SLBP) also known as phosphorene is a recently introduced two-dimensional material with unique structure and promising physical properties that has drawn considerable attention in the field of nanodevices. This structure demonstrates a high anisotropy in mechanical and thermal behavior along zigzag (ZZ) and armchair (AC) principal in-plane directions. Here in this study, it is shown that implementing shear strain on 10 nm × 50 nm SLBP nanoribbons (SLBPNRs) along ZZ and AC directions, the anisotropy leads to different corrugated patterns on the pristine structure. Applying non-equilibrium molecular dynamics under a parameterized Stillinger-Weber potential for modelling SLBP, thermal conductivity (TC) behavior of the sheared SLBPNRs with corrugated patterns are examined. The results show a higher amplitude and wavelength of the corregations on the ZZ-aligned SLBPNRs, which is around two times higher than that of AC-aligned counterparts. Although, it is also shown that unlike some other 2D materials, such as graphene, the wrinkling does not have such a significant effect on TC of SLBP. The phonon density of states results obtained in this work as well as phonon dispersion curves by first-principle calculations in other works concrete this finding. The results show small frequency shifts in both high- and low-frequency phonons, which are not strong enough to affect TC in SLBPNRs. This interesting thermal property of SLBP under shear strain suggests the great potential application of these corrugated structures in nanodevices without any loss of TC abilities.