A period-varying folded waveguide is formed by varying the period of a folded waveguide. It has the advantages of the space harmonic selectivity and the wide bandwidth. However, the regularities of the variety of these period-varying folded waveguides are unavailable from the published papers. In order to solve this problem, the principle of the space harmonic selectivity of a period-varying folded waveguide is analysed, and the conditions to select the space harmonic for this slow wave system are obtained. In addition, the space harmonic selectivities for a linear period-varying folded waveguide and a hyperbolic sine-varying period folded waveguide are also analysed as examples.