Construction of conductive coordination polymers (CPs) has already become an attractive strategy for the development of organic-inorganic hybrid functional materials with specific electrical performance, due to the great diversity and tunability of the chemical structures, electronic structures, as well as the functions they can offer. Here, we demonstrate a novel highly conductive CP based on silver (I) and benzenehexathiol (BHT), (Ag3BHT)n, which displays a different chemical stoichiometry and structural topology compared to the previously reported (Ag5BHT)n. Detailed structural analysis shows that this is caused by the unintentional oxidation of the ligand molecules during the CP formation process. (Ag3BHT)n displays an electrical conductivity of 39 S cm-1 at room temperature. Ultraviolet photoelectron spectroscopy characterization and density functional theory calculation reveal that its highly conducting behavior comes from the highly doped character of (Ag3BHT)n. In addition, band structure calculation proposed an unusual double Dirac cone. This work emphasizes the importance of the ligand oxidation strategy, which can greatly enrich the family of conductive CPs based on BHT and other noninnocent ligands.