It is widely accepted that plant peroxidases (EC 1.11.1.7) can catalyze the generation of superoxide anion upon oxidation of substrates in the presence of hydrogen peroxide. Similarly, recent studies have shown that peptides derived from human prion protein (PrP) catalyses the generation of superoxide coupled to oxidation of neurotransmitters and their analogues. As human PrP possesses four putative copper-binding regions, the binding to copper confers the catalytic activities to PrP and derived peptides. Recent demonstrations suggested that PrP-derived copper-binding peptides catalyze the generation of superoxide in peroxidative manner involving hydrogen peroxide as electron acceptor and aromatic compounds or phenolics as electron donors. The least components required for the reaction were shown to be (i) short peptides with copper-binding capability, (ii) copper ions, (iii) hydrogen peroxide, and (iv) amines or phenolics. Notably, tyrosine residue(s) on PrP itself can be a good phenolic substrate, thus the superoxide-generating reaction could be completed within copper-bound PrP supplied with hydrogen peroxide. According to earlier studies, at least single histidine (His or H) residue is required for binding of copper, and the catalytically active copper-binding motif within PrP-derived peptides was determined to be X-X-H (where X can be any amino acids followed by His). This review covers the latest results performing and explaining the mechanism of catalytic activities found in copper-bound short peptides derived from PrPs, by comparing the mechanism for the reactions catalyzed by natural plant peroxidase. Furthermore, chemical and biological approaches for designing the novel small-sized artificial enzymes mimicking the natural peroxidase are described.