Coded aperture imaging spectrometer based on the concept of compressed sensing can acquire the spectral diagram of object. Coded aperture spectral data restoration reconstructs three-dimensional data cube from two-dimensional coded image. The two-step iterative shrinkage/thresholding algorithms were derived from the iterative shrinkage threshold algorithm and weighted iterative shrinkage algorithm. Recovering coded aperture spectral data using the two-step iterative shrinkage/thresholding algorithms obtained the three-dimensional spectral data cube successfully.