A composite cathode material comprised of a polyacetylene derivative with pendant TEMPO electro-active groups and graphite has been obtained and successfully utilized in a rechargeable battery against a Li anode. The battery has an initial specific discharge capacity of 102.6 mAh/g and an initial specific energy capacity of 315.9 mWh/g. This specific energy capacity is very high compared to today's conventional lithium-ion batteries with cathodes made of LiFePO4, LiCoO2, LiMnO2, etc. The battery has retained 77% of its energy capacity after 40 charge–discharge cycles.