Two copper coordination compounds bearing an N,N’-dibenzylethylenediamine ligand, namely [Cu3L(CH3COO)6]n (1) and [(CuCl4)∙(C6H5CH2NH2CH2)2] (2) (L = N,N’-dibenzylethylenediamine) were synthesized by the ethanol refluxing method. Powder X-ray diffraction (PXRD), infrared spectra (IR), elemental analyses, and single crystal X-ray diffraction were used to characterize and verify their structures. Structural analyses showed that the asymmetric unit of compound (1), composed of two Cu(II) cations, three acetate anions, and half of the ligand, was bridged by one acetate to obtain an infinite 1D chain structure. The analyses further showed that the asymmetric unit of compound (2), composed of two crystallographically independent [C6H5CH2NH2CH2]+ units, four chloride anions, and one central Cu(II) cation is connected into an infinite 2D network structure by the hydrogen bonding interactions. The copper compounds were used to catalyze the decomposition of H2O2, and the results showed that both of the compounds exhibited excellent catalytic activities under optimized conditions.