Two ethylene–vinyl acetate (EVA) copolymers containing 10 and 25 wt.% vinyl acetate (EVA10 and EVA25) were utilized to explore the effect of molecular polarity on the formation of conductive carbon nanotube (CNT) network in EVA melt under an electric field. Because of the different interfacial energy, it was supposed to be stronger molecular chain-CNT interaction in CNT/EVA25 than that in CNT/EVA10. The critical time for conductive CNT network formation decreased with annealing temperature, filler loading and EVA polarity. The activation energy of conductive CNT network formation (93.9 kJ/mol) in CNT/EVA10 is lower than that (104.7 kJ/mol) in CNT/EVA25. By a thermodynamic percolation model, the percolation threshold at the equilibrium state was about 0.19 vol.% for CNT/EVA10, while it rose to 0.27 vol.% for CNT/EVA25. Morphological observation showed a high degree of CNT alignment in CNT/EVA10 compared to CNT/EVA25 after application of an electric field. The results suggested the strong CNT–EVA chain interaction and higher viscosity of polymer matrix limited the CNT alignment and the conductive network tended to form easily in EVA melt with a low chain polarity.