Hyperspectral imaging that obtains the spatial-spectral information of a scene has been extensively applied in various fields but usually requires a complex and costly system. A single-pixel detector based hyperspectral system mitigates the complexity problem but simultaneously brings new difficulties on the spectral dispersion device. In this work, we propose a low-cost compressive single-pixel hyperspectral imaging system with RGB sensors. Based on the structured illumination single-pixel imaging configuration, the lens-free system directly captures data by the RGB sensors without dispersion in the spectral dimension. The reconstruction is performed with a pre-trained spatial-spectral dictionary, and the hyperspectral images are obtained through compressive sensing. In addition, the spatial patterns for the structured illumination and the dictionary for the sparse representation are optimized by coherence minimization, which further improve the reconstruction quality. In both spatial and spectral dimensions, the intrinsic sparse properties of the hyperspectral images are made full use of for high sampling efficiency and low reconstruction cost. This work may introduce opportunities for optimization of computational imaging systems and reconstruction algorithms towards high speed, high resolution, and low cost future.