A bicontinuous cubic (Cubbi) liquid crystalline (LC) phase consisting of three dimensional (3D) conducting networks is a promising structural platform for ion-conductors. For practical applications using this fascinating LC structure, it is necessary to suppress crystallization at room temperature (RT). Herein, we report the Cubbi structure at RT and the morphologyâdependent conduction behavior in ionic samples of a non-crystallizable dendritic amphiphile. In the molecular design, branched alkyl chains were used as an ionophobic part instead of crystallizable linear alkyl chains. Two ionic samples with Cubbi and hexagonal columnar (Colhex) LC phases at RT were prepared by adding different amounts of lithium salt to the amphiphile. Impedance analysis demonstrated that the Cubbi phase contributed to the faster ion-conduction to a larger extent than the Colhex phase due to the 3D ionic networks of the Cubbi phase. In addition, the temperatureâdependent impedance and electric modulus data provided information regarding the phase transition from microphase-separated phase to molecularly mixed liquid phase.