Blue phases are three-dimensional self-assembly structures of liquid crystals with a lattice of line defects. They have attracted considerable interest as photonic materials. It is well known that blue phases occur in cholesteric liquid crystals (CLCs) under certain thermodynamic conditions; however, recent studies have indicated that confining surfaces may induce distinctive structural changes. For example, in a previous study, a quasi-two-dimensional (Q2D) confinement system was investigated with the aid of numerical calculations, and a stable Q2D Skyrmion structure was attained. Here, we performed molecular simulations to investigate the CLC phase behavior at the molecular scale for a quasi-one-dimensional (Q1D) nanotube system. Various morphological behaviors of CLCs were observed by changing the temperature and the radius of the nanotubes. In particular, we discovered a self-assembled structure with cylindrical (or ring-like) defects rather than lines by introducing a novel local orientation analysis. Our simulation results show that the self-assembly of CLCs offers a guide to control the intensity in Q1D systems and fundamental knowledge for their application to optical devices.