A protein complex consisting of the serine protease PCSK9 (proprotein convertase subtilisin/kexin-9) and a low-density lipoprotein receptor (LDLR). Interaction typically occurs through the epidermal growth factor-like repeat A (EGF-A) domain of the LDLR, and complex formation promotes degradation of the LDLR through the endosome/lysosome pathway.