Frequency-selective surface (FSS) is a two-dimensional periodic structure consisting of a dielectric substrate and the metal units (or apertures) arranged periodically on it. When manufacturing the substrate, its thickness and dielectric constant suffer process tolerances. This may induce the center frequency of the FSS to shift, and consequently influence its characteristics. In this paper, a bandpass FSS structure is designed. The units are the Jerusalem crosses arranged squarely. The mode-matching technique is used for simulation. The influence of the tolerances of the substrate’s thickness and dielectric constant on the center frequency is analyzed. Results show that the tolerances of thickness and dielectric constant have different influences on the center frequency of the FSS. It is necessary to ensure the process tolerance of the dielectric constant in the design and manufacturing of the substrate in order to stabilize the center frequency.