In this work, we use molecular dynamics simulations to study the responses of the configuration of single-strand DNA (ssDNA) within a carbon nanotube (CNT) and the concomitant ion flow to a single modified base, i.e., benzoimidazole (Bzim)-modified 5-hydroxymethyl cytosine (5hmC). Our simulation results show the Bzim-modified 5hmC can considerably increase the ion flow through a single-walled carbon nanotube (SWCNT), despite its larger size, which is consistent with prior experimental results. This phenomenon is attributed to enhanced adsorption of DNA to the interior wall of the CNT driven by the Bzim-modified 5hmC, leading to a reduced steric effect on ion transport through the CNT. As revealed in this work, the distribution of ssDNA can be affected by limited change in the interactions with the CNT surface. Such behavior of ssDNA within small-sized CNTs can be exploited to further improve the sensitivity of nanopore detection.