In this work, we investigated the mimetic enzyme activity of two-dimensional (2D) Pd-based nanostructures (e.g. Pd nanosheets, Pd@Au and Pd@Pt nanoplates) and found that they possess intrinsic peroxidase-, oxidase- and catalase-like activities. These nanostructures were able to activate hydrogen peroxide or dissolved oxygen for catalyzing the oxidation of organic substrates, and decompose hydrogen peroxide to generate oxygen. More systematic investigations revealed that the peroxidase-like activities of these Pd-based nanomaterials were highly structure- and composition-dependent. Among them, Pd@Pt nanoplates displayed the highest peroxidase-like activity. Based on these findings, Pd-based nanostructures were applied for the colorimetric detection of H2O2 and glucose, and also the electro-catalytic reduction of H2O2. This work offers a promising prospect for the application of 2D noble metal nanostructures in biocatalysis.