Abstract: Wideband spectrum sensing for GHz-wideband spectrum generally in a large number of sample points and a high computational load. Using the signal spectrum sparsity, Sparse Fourier Transform computes wideband signal spectrum efficiently and its computational complexity is lower than the FFT algorithms. In this paper, one of Sparse Fourier Transform algorithm, Hash mapping is studied in detail and spectrum permutation property is proved. In order to reduce the probability of missing sampling points, the signal spectrum is permuted and the signal is window weighted. Then, the signal is aliased in time-domain to realize the spectral down-sampling. Finally, using inverse Hash mapping and voting loop the original spectrum is recovered accurately. The simulation results show that the computational time of this method is about 19 times and 47 times lower than that of the OMP algorithm when the sampling length is increased from 1024 points to 2048 points.