Existing structured illumination microscopy (SIM) allows super-resolution live-cell imaging in few color channels that provide merely morphological information but cannot acquire the sample spectrum that is strongly relevant to the underlying physicochemical property. We develop hyperspectral SIM which enables high-speed spectral super-resolution imaging in SIM for the first time. Through optically mapping the three-dimensional (, , and λ) datacube of the sample to the detector plane, hyperspectral SIM allows snapshot spectral imaging of the SIM raw image, detecting the sample spectrum while retaining the high-speed and super-resolution characteristics of SIM. We demonstrate hyperspectral SIM imaging and reconstruct a datacube containing 31 super-resolution images of different wavelengths from only 9 exposures, achieving a 15 nm spectral resolution. We show time-lapse hyperspectral SIM imaging that achieves an imaging speed of 2.7 s per datacube-31-fold faster than the existing wavelength scanning strategy. To demonstrate the great prospects for further combining hyperspectral SIM with various spectral analysis methods, we also perform spectral unmixing of the hyperspectral SIM result while imaging the spectrally overlapped sample.