Vascular adhesion protein-1 (VAP-1), also known as plasma amine oxidase or semicarbazide-sensitive amine oxidase, is an enzyme that degrades primary amines to aldehydes with the formation of hydrogen peroxide and ammonia. Among others, it plays a role in inflammatory processes as it can mediate the migration of leukocytes from the blood to the inflamed tissue. We prepared a series of ω-(5-phenyl-2H-tetrazol-2-yl)alkyl-substituted glycine amides and related compounds and tested them for inhibition of purified bovine plasma VAP-1. Compounds with submicromolar activity were obtained. Studies on the mechanism of action revealed that the glycine amides are substrate inhibitors, i.e., they are also converted to an aldehyde derivative. However, the reaction proceeds much more slowly than that of the substrate used in the assay, whose conversion is thus blocked. Examination of the selectivity of the synthesized glycine amides with respect to other amine oxidases showed that they inhibited diamine oxidase, which is structurally related to VAP-1, but only to a much lesser extent. In contrast, the activity of monoamine oxidase A and B was not affected. Selected compounds also inhibited VAP-1 in human plasma. The IC50 values measured were higher than those determined with the bovine enzyme. However, the structure–activity relationships obtained with the glycine amides were similar for both enzymes.