Fabry-Pérot cavity antennas are a well-known solution to increase directivity. However, manufacturing tolerances tend to negatively influence the antenna performance, particularly as frequency increases. This paper proposes a frequency selective surface design for a dual band Fabry-Pérot cavity antenna (FPCA), specifically for Ka-band, which favors fabrication reliability. The FSS is formed by a single substrate with double-side metallization. As an example 11 FSS elements all tuned for Ka-band operation are designed in order to obtain a different set of directivities at each frequency band (20 and 30 GHz). A prototype was manufactured.