Abstract: This article has put forward a numerical method which could compute dispersion curves in an arbitrary coaxial periodic slow-wave structure, based on field-matching method and Fourier series theory. This numerical method has strong universality and expansibility in designing slow-wave structures. Using this numerical method, the dispersion curves of the coaxial sinusoidal ripple waveguide and the coaxial dual sinusoidal ripples waveguide were computed by programming Matlab codes, and their dispersion characteristics were analyzed and discussed. The dispersion curves of the coaxial disk-loaded waveguide were computed by this numerical method as an example. The numerical results were compared with the simulated results of a multidimensional full electromagnetic software, and the reliability o