The dynamics and structure of the hydrogen-bond network in confined water are of importance in understanding biological and chemical processes. Recently, terahertz (THz) time domain spectroscopy was widely applied for studying the kinetics of molecules and the hydrogen-bond network in water. However, the characteristics of the THz spectroscopy varying with respect to the confinement and the mechanism underlying the variation are still unclear. Here, on the basis of molecular dynamics simulations, the relationship between the anisotropic dielectric relaxation and the structure of the water confined in a carbon nanotube (CNT) was investigated. The results show that there are two preferred hydrogen-bond orientations of the confined water in the nanotube: (1) parallel to the CNT axis and (2) perpendicular to the CNT axis, which are clearly different. Moreover, the response of the orientations to the increment of the CNT diameters is opposite, leading to the opposite variations of the dielectric relaxation times along the two directions. The anisotropy in the relaxation time can be presented by the anisotropic dielectric permittivity which is able to be observed through THz spectroscopy. The anormal behaviors above are attributed to the special structure of the water close to the nanotube wall due to the confinement and hydrophobicity of CNT. These studies contribute an important step in understanding the THz experiments of water in nanoscales, and designing a chamber for specific chemical and biological reactions by controlling the diameters and materials of the nanotube.