Local mean decomposition (LMD) method is a new adaptive signal processing method. Teager energy operator is an algorithm to solve the signl instantaneous energy, which can effectively extract instantaneous energy of nonlinear signals. Combined with the advantages of two methods, a method of power spectrum estimation is proposed based on LMD- Teager transformation. The principle and steps of the method are presented and the physical meaning of power spectrum estimation is discussed. On the basis of the comparison with the fast Fourier tranform algorithm (FFT) method and wavelet transform, A short data sequence and non-stationary signal are simulated to verify the effect of the proposed method. The results show that the proposed method breaks through the difficulty that the FFT method just can process the stationary signal, and it is more suitable for non-stationary signal. The length of the required data is shorter than that in Fourier method, and the analysis accuracy and resolution are better than that of traditional Fourier method and wavelet transform.