Despite the development of therapeutic modalities to treat cancer, multidrug resistance (MDR) and incomplete destruction of deeply embedded lung tumors remain long-standing problems responsible for tumor recurrence and low survival rates. Therefore, developing therapeutic approaches to treat MDR tumors is necessary. In this study, nanodrugs with enhanced intracellular drug internalization were identified by the covalent bonding of carbon nanotubes of a specific nano size and doxorubicin (DOX). In addition, carbon nanotube conjugated DOX (CNT-DOX) sustained in the intracellular environment in multidrug-resistant tumor cells for a long time causes mitochondrial damage, suppresses ATP production, and results in the effective therapeutic effect of drug-resistant tumors. This study identified that H69AR lung cancer cells, an adriamycin (DOX) drug-resistant tumor cell line, did not activate drug resistance function on designed nano-anticancer drugs with a specific nano size. In summary, this study identified that the specific size of the nanodrug in combination with DOX overcame multidrug-resistant tum cells and inhibiting ATP by mitochondrial damage.