Cancer remains among the world's top devastating diseases, with millions of lives been affected each year. Conventional anticancer therapies are often far from ideal due to non-selective biodistribution. Therefore, the carbon nanotube (CNT) has been developed as a drug carrier for targeting specific cancer cells. In this work, we applied computer modeling approaches to investigate the interactions of single-wall carbon nanotube (SWCNT) with three different anticancer drugs: doxorubicin (DOX), Bendamustine (BEN), and Carmustine (CAR). Here we find physicochemical characteristics from the ligands that can contribute to a higher affinity towards the CNT, such as the presence of halogen substituents and the positively charged cation. On the other hand, the presence of anions groups, such as carboxylate, can decrease the interaction of the ligands and CNT. The binding free energy results indicate the SWCNT(15,15) with a diameter of 20.3 Å as the most favorable for encapsulating drugs ranging from 12 to 39 heavy atoms. The basic knowledge obtained from this study is expected to contribute to the molecular understanding of drug-loaded SWCNT for the development of a more efficiently anticancer drug carrier.