In this paper, cylindrically-varying photonic crystal waveguides (PCWs) with high-index cores are first proposed and analyses are performed for guiding characteristics of the waveguides. Exact analyses for the axial and transverse electromagnetic field components of guided modes are performed for guiding characteristics of the proposed waveguide. Since the difference between two refractive index values in the periodically-repeating rings of the cladding region can be large, it is necessary to apply a vectorial approach instead of a scalar-wave approximation to analyze a cylindrically-varying PCW. For verification and usage in design and manufacturing processes, an algorithm regarding the rigorous full-vectorial finite difference method is also formulated and utilized to perform the computer-calculation of the waveguide transmission characteristics. Electromagnetic fields are heavily confined close to the central region for the cylindrically-varying PCWs with a high-index core. Computer-analyses of effective mode area indicate that the PCWs designed with 4 or 8 layers provide about 10 times smaller effective areas, compared with effective mode areas of conventional optical fibers.