Abstract: This paper propose a method to estimate the signal power spectral density using the sub-Nyquist sampling data.Firstly,the appropriate Multi-Coset Sampling (MCS) mode is used to sample the observed signal.And then,the cross correlation between the output of each channel of MCS system is calculated.Finally,the least squares method or non-negative least squares method is used to directly estimate the signal power spectral density.The simulation results show that the algorithm can effectively reduce the sampling rate with correctly estimating the power spectral density of the radio astronomy signal,and it is not required for the sparsity of the signal.