In the measurement of the radioactivity energy spectrum, due to the low resolution of the detector, the similarity of the atomic energy level in the sample to be tested, and the limitation of the instrument stripping technology, the overlapping phenomenon of full energy peak often occurs, which brings great difficulties to the qualitative or quantitative detection of radionuclides. Conventional separation algorithms generally require complex spectrum transformation or a large number of standard spectrum samples and are not suitable for real-time decomposition of overlapping peaks at on-site of measurement. Therefore, a decomposition method of energy spectrum overlapping peaks based on the Gaussian sharpening method (GSM) is proposed, combining the resolution enhancement capability of the peak sharpening method and the smoothing characteristics of the convolution sliding transformation method, which can quickly identify, locate and resolve overlapping peaks in the γ energy spectrum. Firstly, the Gaussian function is sharpened and normalized and selected the appropriate Gaussian parameters and window width, used as a transformation operator to filter and improve the separation of overlapping peaks through convolution and sliding transformation of the original γ energy spectrum data. Then, the approximate function of the energy spectrum after GSM shaping is solved as the objective function, and several points near the center of the peak position are selected as initial parameters. Finally, the analysis of the characteristic peak parameters of the overlapping peaks is carried out by the method of nonlinear fitting. In the experiment, we first verified the invariance of the peak position and peak area eigenvalues before and after GSM shaping, and then the GSM was verified in the overlapping peak energy spectrum and the MCNP simulated¹³¹I, ¹³⁷Cs, ²¹⁴Bi, ²⁰⁶Bi and ²⁶Al mixed radioactive source γ energy spectrum. The experimental results show that GSM has great decomposition ability for the overlapping peak with the resolution better than 0.375 and the SNR better than 40 dB, the relative errors of the peak position and peak area before and after decomposition are within 1% and 4.5%, respectively; For the GSM-processed energy spectrum of γ-ray, the relative error of the position of the overlapping peak is within 1% and that of the single peak is within 0.1%, furthermore, the decomposition result will be more accurate if the half-width in the transformation operator is set close to the energy resolution of the detector. GSM is noise-immune and does not require pre-processing operations such as spectrum smoothing and background subtraction in full-spectrum analysis. Besides, it consumes less computing resources and has high-resolution accuracy, which is convenient for embedded real-time spectrum analysis of energy spectrum measurement system and has practicability for quick on-site analysis of energy spectrum in radioactive measurement.