The information dimension obtained by multispectral ghost imaging is more abundant than in single-band ghost imaging. Existing multispectral ghost imaging systems still meet some shortages, such as complex structure or reconstruction time-consuming. Here, an approach of cosinusoidal encoding multiplexed structured illumination multispectral ghost imaging is proposed. It can capture the multispectral image of the target object within one projection cycle with a single-pixel detector while maintaining high imaging efficiency and low time-consuming. The core of the proposed approach is the employed novel encoding strategy which is apt to decode and reconstruct the multispectral image via the Fourier transform. Specifically, cosinusoidal encoding matrices with specific frequency characteristics are fused with the orthogonal Hadamard basis patterns to form the multiplexed structured illumination patterns. A broadband photomultiplier is employed to collect the backscattered signals of the target object interacted by the corresponding structured illumination. The conventional linear algorithm is applied first to recover the mixed grayscale image of the imaging scene. Given the specific frequency distribution of the constructed cosinusoidal encoding matrices, the mixed grayscale image can be converted to the frequency domain for further decoding processing. Then, the pictures of multiple spectral components can be obtained with some manipulations by applying Fourier transform. A series of numerical simulations and experiments verified our proposed approach. The present cosinusoidal encoding multiplexed structured illumination can also be introduced in many other fields of high-dimensional information acquisition, such as high-resolution imaging and polarization ghost imaging.