Vascular adhesion protein-1 (VAP-1) is a primary amine oxidase and a drug target for inflammatory and vascular diseases. Despite extensive attempts to develop potent, specific, and reversible inhibitors of its enzyme activity, the task has proven challenging. Here we report the synthesis, inhibitory activity, and molecular binding mode of novel pyridazinone inhibitors, which show specificity for VAP-1 over monoamine and diamine oxidases. The crystal structures of three inhibitor VAP-1 complexes show that these compounds bind reversibly into a unique binding site in the active site channel. Although they are good inhibitors of human VAP-1, they do not inhibit rodent VAP-1 well. To investigate this further, we used homology modeling and structural comparison to identify amino acid differences, which explain the species-specific binding properties. Our results prove the potency and specificity of these new inhibitors, and the detailed characterization of their binding mode is of importance for further development of VAP-1 inhibitors.