The frequency selective surfaces(FSSs) with chessboard patterns are proposed and designed for the first time in this paper. We proposed the design parameters like slot and patch size, gap between slots or patches, and dielectric thickness of FSS chessboard unit cell proposed in this paper. Also, we found that the variation of design parameters can be used to control the frequency transmission characteristics like the resonant frequency or bandwidth of FSS. To validate the proposed FSS, we fabricated the proposed FSS with the use of 1.0mm FR4 for the bandpass operation at X-band and measured the transmission characteristics. From the results, the proposed FSS with chessboard type can be widely applied to application of the frequency controllable radome design because we can use the design parameters selectively.