Molecular dynamics (MD) simulations have been carried out to understand the binding mechanism of various chiral single-walled carbon nanotubes (SWCNTs) and single-stranded DNA (ssDNA) of four different nucleobase sequences (i.e., ssdA(14), ssdT(14), ssdG(14), and ssdC(14), where, A, T, G, and C are adenine, thymine, guanine, and cytosine, respectively) in aqueous media at room temperature (300 K) and atmospheric pressure (1 atm). The simulations studies reveal that ssDNA undergoes rapid structural changes and wrap around the SWCNTs via π-stacking interactions between SWCNT's wall and the nucleobases of ssDNA. Our computations demonstrate that the length of the ssDNA plays an important role during the wrapping process. Moreover, it suggests that the length of the sequence should be proportional to the diameter of the SWCNT, in order to overcome the intralocked π-stacking interactions between the nucleobases of ssDNA sequence. Also, in our classical MD simulation, we do not observe the correlation between the diameter of SWCNTs and the sequences of ssDNA, which indicates the importance of electronic factors of these systems. In order to understand the electronic contributions of these systems, the quantum calculations have been performed at Hartree-Fock level for the 17 ns MD simulated structures. The quantum chemical calculations provide evidence that the highly stable ssDNA@SWCNT hybrid possesses a larger HOMO-LUMO gap.