In an organic–inorganic hybrid compound, neighbouring [Co(CN)₆]³⁻ anionic units are linked by Li⁺ cations through the cyanide groups in a trans mode, forming a one-dimensional zigzag chain structure extending along the c axis. A three-dimensional supra­molecular network is formed through hydrogen-bonding inter­actions and is further stabilized by weak CNπ inter­actions between the cyanide groups and the imidazolium cations.