Dual-ion batteries (DIBs) inherently suffer from limited energy density due to insufficient anion storage capacity of typical graphite cathodes. Herein, we propose a new design strategy to effectively tackle this issue via employing locally ordered graphitized carbon (LOGC) cathodes. Quantum mechanical modeling suggests that strong anion-anion repulsion and severe expansion at the deep-charging stage raise the anion intercalation voltage, therefore only part of the theoretical anion storage sites in graphite is accessible. The LOGC interconnected with disordered carbon is predicted to weaken the interlaminar van der Waals interaction, while disordered carbons not only interconnect the dispersed nano-graphite but also partially buffer severe anion-anion repulsion and offer extra capacitive anion storage sites. As a proof-of-concept, ketjen black (KB) with the typical feature of LOGC is selected as a model cathode for a potassium-based DIB (KDIB). The KDIB delivers an unprecedentedly high specific capacity of 232 mAh g -1 at 50 mA g -1 , a good rate capability of 110 mAh g -1 at 2000 mA g -1 and excellent cycling stability of 1000 cycles without obvious capacity fading.