The invention discloses a hyperspectral image acquisition imaging system and a control method based on compressive sensing. Firstly, a digital mirror device (DMD) performs compressive sampling on image information; secondly, a liquid crystal tunable filter (LCTF) controls permeable light wavelength and spectral resolution, and then an area array charge coupled device (CCD) acquires light intensity information; and finally, an analog adder and an ADC (Analog-to-Digital Converter) perform signal processing, and store the processed digital quantity in a memory. The hyperspectral image acquisition imaging system and the control method based on the compressive sensing provided by the invention realize signal sampling and compression, and make sampling data much smaller than the amount of data required by the traditional Nyquist sampling theory; and also solve the problem of waste of resources caused by transmission pressure and a large amount of redundant information due to hyperspectral data acquisition.