Bicontinuous porous materials, which possess 3D interconnected pore channels facilitating a smooth mass transport, have attracted much interest in the fields of energy and catalysis. However, their synthesis remains very challenging. We report a general approach, using polymer cubosomes as the template, for the controllable synthesis of bicontinuous porous polymers with an ordered single primitive (SP) cubic structure, including polypyrrole (SP-PPy), poly-m-phenylenediamine (SP-PmPD), and polydopamine (SP-PDA). Specifically, the resultant SP-PPy had a unit cell parameter of 99 nm, pore diameter of 45 nm, and specific surface area of approximately 60 m2·g-1. As a proof of concept, the I2-adsorbed SP-PPy was employed as the cathode materials of newly emerged Na-I2 batteries, which delivered a record-high specific capacity (235 mA·h·g-1 at 0.5 C), excellent rate capability, and cycling stability (with a low capacity decay of 0.12% per cycle within 400 cycles at 1 C). The advantageous contributions of the bicontinuous structure and I3- adsorption mechanism of SP-PPy were revealed by a combination of ion diffusion experiments and theoretical calculations. This study opens a new avenue for the synthesis of porous polymers with new topologies, broadens the spectrum of bicontinuous-structured materials, and also develops a novel potential application for porous polymers.