This paper concerns the development of an electrochemical biosensor for the determination of Aβ16–23′ and Aβ1–40 peptides. The His-tagged V and VC1 domains of Receptor for Advanced Glycation end Products (RAGE) immobilized on a gold electrode surface were used as analytically active molecules. The immobilization of His6–RAGE domains consists of: (i) formation of a mixed layer of N-acetylcysteamine (NAC) and the thiol derivative of pentetic acid (DPTA); (ii) complexation of Cu(II) by DPTA; (iii) oriented immobilization of His6–RAGE domains via coordination bonds between Cu(II) sites from DPTA–Cu(II) complex and imidazole nitrogen atoms of a histidine tag. Each modification step was controlled by cyclic voltammetry (CV), Osteryoung square-wave voltammetry (OSWV), and atomic force microscopy (AFM). The applicability of the proposed biosensor was tested in the presence of human plasma, which had no influence on its performance. The detection limits for Aβ1–40 determination were 1.06 nM and 0.80 nM, in the presence of buffer and human plasma, respectively. These values reach the concentration level of Aβ1–40 which is relevant for determination of its soluble form in human plasma, as well as in brain. This indicates the promising future application of biosensor presented for early diagnosis of neurodegenerative diseases.