Aming at the overlapping peaks in spectrum analysis, a novel method of curve fitting based on Gaussian function is presented to resolve the overlapping peaks. The theory of curve fitting is introduced firstly, and then an algorithm is proposed based on both the minimum separable peak peak interval and the curve fitting error. In the peak positioning, a gradually strict strategy is introduced to exclude the fake peaks. The resolution of several kinds of overlapping peaks with computer simulated noise has been performed and discussed in details. The calculated results indicate that the peak positions can be extracted effectively, even in the case of serious overlapped, and clearly show the effectiveness of the proposed method.