The pro-protein convertase furin is a highly specific serine protease involved in the proteolytic maturation of many proteins in the secretory pathway. It also activates surface proteins of many viruses including the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Furin inhibitors effectively suppress viral replication and thus are promising antiviral therapeutics with broad application potential. Polybasic substrate-like ligands typically trigger conformational changes shifting furin's active site cleft from the OFF-state to the ON-state. Here, we solved the X-ray structures of furin in complex with four different arginine mimetic compounds with reduced basicity. These guanylhydrazone-based inhibitor complexes showed for the first time an active site-directed binding mode to furin's OFF-state conformation. The compounds undergo unique interactions within the S1 pocket, largely different compared to substrate-like ligands. A second binding site was identified at the S4/S5 pocket of furin. Crystallography-based titration experiments confirmed the S1 site as the primary binding pocket. We also tested the proprotein convertases PC5/6 and PC7 for inhibition by guanylhydrazones and found an up to 7-fold lower potency for PC7. Interestingly, the observed differences in the Ki values correlated with the sequence conservation of the PCs at the allosteric sodium binding site. Therefore, OFF-state-specific targeting of furin can serve as a valuable strategy for structure-based development of PC-selective small-molecule inhibitors.