Quinoid compounds are important candidates of organic active materials for lithium-ion batteries. However, its high solubility to organic electrolyte solutions and low redox potential are known as their major drawbacks. To circumvent these issues, we have designed and synthesized a tandem-tetracyanoquinonedimethane type cathode-active material, 11,11,12,12,13,13,14,14-octacyano-1,4,5,8-anthradiquinotetramethane (OCNAQ), that has four redox sites per molecule, high redox potential and suppressed solubility to electrolyte solution. Synthesized OCNAQ has been found to have two-step redox reactions by cyclic voltammetry, and each step consists of two-electron reactions. During charge-discharge tests using selected organic cathode-active materials with a lithium metal anode, the cell voltages obtained from OCNAQ are higher than those for 11,11-dicyanoanthraquinone methide (AQM) as expected, due to the strong electron-withdrawing effect of the cyano groups. Unfortunately, even with the use of the organic active material, the issue of dissolution to the electrolyte solution cannot be suppressed completely; however, appropriate choice of the electrolyte solutions, glyme-based electrolyte solutions in this study, give considerable improvement of the cycle retention (98% and 56% at 10 and 100 cycles at 0.5C, respectively). The specific capacity and energy density obtained in this study are 206 mAh g−1 and 554 mWh g−1 with respect to the cathode active material.