Introduction of mechanical flexibility into proton-conducting coordination polymers (CPs) is in high demand for future protonic applications such as fuel cells and hydrogen sensors. Although such mechanical properties have been primarily investigated in one-dimensional (1D) CPs, in this study, we successfully fabricated highly flexible free-standing CP membranes with a high surface-to-volume ratio, which is beneficial for enhanced performance in the aforementioned applications. We fabricated a layered CP, Cu2 (NiTCPP) (H4 (H2 TCPP); 5,10,15,20-tetrakis(4-carboxyphenyl) porphyrin), in which a two-dimensional (2D) square grid sheet composed of tetradentate nickel porphyrins and paddlewheel-type copper dimers was connected to each other by weak van der Waals forces. The mechanical flexibility was evaluated by bending and tensile tests. The flexural and Young's moduli of the membrane were significantly higher than those of conventional Nafion membranes. Electrochemical impedance spectroscopy analysis revealed that the in-plane proton conductivity of the membrane was maintained even under applied bending stress. Because the X-ray diffraction analysis indicates that the proton-conducting pathway through the hydrogen bonding network remains intact during the bending operation, our present study provides a promising strategy for the fabrication of new and advanced 2D CPs without using substrates or additional polymers for protonic devices.