Herein, we create a unique double percolated conductive structure in the carbon nanotube (CNT)/ethylene vinyl acetate (EVA)/ultrahigh-molecular-weight polyethylene (UHMWPE) composite, in which CNTs are loaded in EVA interior to form interconnected conductive networks (the first percolation) and only 20 wt% CNT-enriched EVA forms a perfect continuous phase in the whole composite (the second percolation). Compared with conventional double percolated CPCs which always require filler-enriched polymer content up to 50 wt%, such a low CNT/EVA content gives rise to an unprecedentedly increased effective CNT concentration in the CNT/EVA/UHMWPE composite. The unique double percolated composite exhibits excellent electrical conductivity comparable to that obtained in CNT-loaded single EVA composite with five times of CNT content. Only 7.0 wt% CNT gives the composite a superior EMI shielding effectiveness of 57.4 dB, much higher than that of mostly reported CNT and graphene based CPCs. Absorption is demonstrated to be the primary shielding mechanism due to the numerous interfaces between UHMWPE domains and CNT/EVA layers that benefit multiple reflection, scattering and adsorption of the incident microwaves. The construction of unique double percolated structure in our work provides promising strategy for developing cost-effective and high-performance CPCs for use as efficient EMI shielding materials.