The large-scale applications of energy storage systems call for large demand of low cost materials with high capacities and high rate performance. Conjugated organic/polymeric materials have attracted great attention owing to their flexibility, abundance resources, low cost and the tunability of performance through molecular design. However, it is still challenging to develop novel materials with both high capacities and high rate performance. Here, a novel conjugated polymer with unique ladder-structure is developed and applied in both organic sodium-ion batteries (OSIBs) and hybrid supercapacitors (HSCs). The as-prepared conjugated polymer/graphene composites delivered a large specific capacity of ~245 mAh g-1 at 0.2 A g-1 for OSIBs, and excellent rate performance (capacity of ~210 mAh g-1 at 1 A g-1 (~3.3C)) and cycle stabilities (>1400 cycles) with a capacity retention of 98%. Moreover, the fast charge transfer and rapid ionic diffusion of PYT-TABQ/rGO electrodes made it promising as electrodes for high-energy-density supercapacitors. The electrodes displayed high specific pseudocapacitance capacitance of 312.5 F g-1 with high capacity retention of 94.5% even after 10,000 cycles at 10 A g-1. This work provides an efficient approach to design multi-functional organic/polymeric electrodes toward the next-generation advanced high performance energy storage devices.