We use molecular dynamics (MD) simulations to show that a DNA-like double helix of two poly(acetylene) (PA) chains can form inside single-walled carbon nanotubes (SWNTs). The computational results indicate that SWNTs can activate and guide the self-assembly of polymer chains, allowing them to adopt a helical configuration in a SWNT through the combined action of the van der Waals potential well and the π-π stacking interaction between the polymer and the inner surface of SWNTs. Meanwhile both the SWNT size and polymer chain stiffness determine the outcome of the nanostructure. Furthermore, we also found that water clusters encourage the self-assembly of PA helical structures in the tube. This molecular model may lead to a better understanding of the formation of a double helix biological molecule inside SWNTs. Alternatively, it could form the basis of a novel nanoscale material by utilizing the 'empty' spaces of SWNTs.