Carbon nanotubes (CNTs) have shown growing potential applications in the fields of biotechnology and biomedicine because of their unique structure and properties. The hollow channels can be used to deliver drug molecules. However, the transport properties of small molecules through the CNT hollow channels are not yet clear. In this study, we will investigate the transport properties of small polar molecules in the ultrashort CNTs embedded in the lipid bilayer using molecular dynamics simulations. By varying the diameter of the CNTs, we find that only water molecules can enter the (6, 6) CNT. Furthermore, the (7, 7) tube exhibits selectivity between dimethyl sulfoxide (DMSO) and urea, whereas both DMSO and water or urea and water can flow in the (8, 8) CNT. Potential of mean force (PMF) calculations confirm that DMSO in the (7, 7) CNT possesses a lower free energy compared with urea. Because of the strong dipolar interaction, DMSO molecules form a single-file chain in (7, 7) CNT, but they are not well ordered in (8, 8) CNT. As comparison, urea molecules are mixed with water molecules in both (7, 7) and (8, 8) CNTs. CNTs exhibit selective transport according to their pore size and the polarity of small molecules. The results may offer new insights into the transport principles of CNTs based on their hollow channels.