Abstract: In present paper, the method of processing the singular points of γ energy spectrum was established by using Lipschitz exponent and wavelet transform. The principle of modulus maximum denoising and the alternating projection reconstruction algorithm proposed by Mallat were analyzed, and the processing model of γ ray energy spectrum data was established. The wavelet transform modulus maximum denoising software was designed based on MATLAB, and the method was simulated and analyzed with the actual-measurement γ ray energy spectrum data. The results show that the method using wavelet transform and alternating projection is good at noise reduction and reconstructing the energy spectrum data.