Chiral metamaterials have attracted great interests in recent years owing to fascinating properties such as negative refraction, strong optical activity, and circular dichroism, which can be applied in many optoelectronic devices. Helix is especially suitable for studying chiral responses as the helical geometry well resembles the feature of circularly polarized light. In this study, we use a helix structure as a model system to demonstrate the general response of circularly polarized light in a three-dimensional dielectric helix nanostructure. The optical characterization is performed based on finitedifference time-domain (FDTD) method and our results show that the helix structure, consisting of dielectric helices arranged in a square lattice, exhibits multiple resonant peaks. The retrieved effective parameters from the complex transmittance and reflectance will be presented and the dispersion characteristics will be discussed based on various geometric parameters. The resonant frequencies can be tuned by structural parameters, and negative permeability can be achieved when the resonances are adjacent in frequencies. Depending on the geometrical arrangements, we will demonstrate the unique optical properties in an anisotropic helix nanostructure. Our analysis yields physical insight into the interaction of circularly polarized light with a three-dimensional chiral nanostructure, and provides design guidelines towards the implementation of all-dielectric photonic metamaterials.