Solid state ionics is a new research field attracting much current attention. One of the most urgent subjects in this field is to create a novel proton conductor, from the viewpoint of developing new energy and energy conservation technologies, including photovoltaic, hydrogen storage and fuel cell technologies. In this paper, we report on a novel proton-conductive organic-inorganic hybrid system, which is a 2-D coordination polymer composed of Cu(II) dimers and bridging ligands R_2dtoa (R_2dtoa=disubstituted dithiooxamide), as shown in Figure 1. Such a metal-dimer system with multi-redox property has a large potentiality for the creation of new-functional and high-performance materials in metal-complex solids. The proton conductivities of R_2dtoaCu (R=H, C_2H_4OH, C_3H_6OH) were measured by a conventional quasi-four-probe method with an impedance analyzer in the frequency range of 40 Hz-4 MHz. The (HOC_2H_4)_2dtoaCu chemically adsorbs hydrogen according to the proton-coupled redox property, which was confirmed by XPS and IR measurements. From the complex-plane impedance plots, all the coordination polymers were found to be highly proton-conductive at room temperature. Among them, H_2dtoaCu exhibits highest proton conduction (〜10^<-2> S cm^<-1>). This value is comparable to that of Nafion, which is famous for a solid electrolyte of fuel cell.