To overcome the problems of traditional multispectral imaging system, such as sophisticated algorithm and time-consuming for reflectance reconstruction, and high cost etc., we present a multispectral imaging system for measuring colors by using LEDs illumination and monochrome high-speed camera. Multiple monochrome LEDs are used to fit lighting source and to ensure that the spectral power distribution of the source is reciprocal of the spectral sensitivity curve of monochrome high-speed camera, and then the spectral reflectance of the object is reconstructed by using the camera response directly. The experimental results show that compared with a spectrophotometer, the method can achieve an average of 2.3 CIELAB color difference for 24 Macbeth ColorChecker chart. The whole system is simple and feasible, and does not need filters, and the spectral reflectance reconstruction algorithm is simple.