Abstract: This article puts forward a numerical method which could compute dispersion curves in an arbitrary axial-symmetric tapered quasi-periodic slow-wave structure, based on field-matching method and Fourier series theory. Using this numerical method, the dispersion curves of a tapered sinusoidal ripple waveguide and a tapered disk-loaded waveguide were computed by programming Matlab codes. The dispersion characteristics of these two typical tapered quasi-periodic slow-wave structures were analyzed and discussed. Numerical results were compared with the simulated results of multidimensional full electromagnetic software, and the reliability of this numerical method was validated. The numerical method has a strong universality and expansibility in designing slow-wave structures, it could also com