The natural color of biological specimens plays a crucial role in body protection, signaling, physiological adaptations, etc. Full-color optical sectioning structured illumination microscopy (OS-SIM) color is a promising approach that can reconstruct biological specimens in three-dimension meanwhile maintaining their natural color. Full-color OS-SIM takes the advantages of rapid imaging speed, compatibility with fluorescence and non-fluorescence samples, compact configuration, and low cost. However, the commonly used HSV-RMS reconstruction algorithm for full-color OS-SIM faces two issues to be improved. One is the RMS (root-mean-square) OS reconstruction algorithm is prone to background noise, and the other is the reconstruction is bound in RGB and HSV color spaces, consuming more reconstructing time. In this paper, we propose a full-color Fourier-OS-SIM method that allows for the OS reconstruction using the high-frequency spectrum of the sample and thus is immune to the low-frequency background noise. The full-color Fourier-OS-SIM directly runs in the RGB color space, providing an easy way to restore the color information. Simulation and experiments with various samples (pollen grains and tiny animals) demonstrate that the full-color Fourier-OS-SIM method is superior to the HSV-RMS method regarding background noise suppression. Moreover, benefiting from the background noise suppression merit, the quantitative morphological height map analysis with the full-color Fourier-OS-SIM method is more accurate. The proposed full-color Fourier-OS-SIM method is expected to find broad applications in biological and industrial fields where the 3D morphology and the color information of objects both need to be recovered.