To solve the problem that common iterative pursuit algorithm has low success rate and precision of spectrum reconstruction in low sampling rate, an improve atom selection method of the spectrum reconstruction in low sampling rate is proposed. The spectrum dictionaries are constructed with AVIRIS and ROSIS hyperspectral data and the compressive sensing hyperspectral reconstruction experiment is conducted. The spectrum reconstruction precision, the sparse component extraction ability, and the success rate and accuracy rate in spectral reconstruction are analyzed in different views, respectively. Experimental results show that the proposed method is much better than conventional matching pursuit algorithms and also superior to the well know high precision method such as FOCUSS and MSBL algorithms.