To eliminate the influence of serious spectra drift and overlapping peaks on analytical accuracy of NaI(Tl) gamma spectra, a global optimization fusion algorithm for correcting and quantitatively analyzing NaI(Tl) gamma spectra was proposed in this paper. By embedding the system transformation based spectral correction algorithm into the full-spectrum analytical model, the optimal spectral drift correction and quantitative analysis of NaI(Tl) gamma spectra were obtained simultaneously using particle swarm optimization without solving overlapped peaks or calculating the peak parameters, even without considering the influence of system energy resolution. The statistically analytical results of the actual measured spectra of a standard volumetric radioactive source show that the maximum relative deviations of radioactive activities of 226Ra, 232Th, and 40K from the known values were 2.74, 1.91, and 3.86%, respectively, and the corresponding uncertainties were 3.86, 2.76, and 6.95%, respectively, which indicates that high analytical accuracy and high precision were obtained using the proposed algorithm. It can be deduced that the fusion algorithm has high stability, reliable statistical performance and low requirements on initial parameters. Also, its procedure is easy to operate, especially suitable for non-expert users. [ABSTRACT FROM AUTHOR]