In nuclear spectrum, Gaussian function least square fitting is a commonly used method. Usually the method has high precision, but it is very much sensitive to noise, which causes that the residual vector is larger near the peak in the Gaussian function. To solve the problem, Gaussian function least square fitting was deduced particularly, and the causes are analyzed. As a result, Gaussian function weighted least square fitting is proposed, i.e., a weight factor, which had an opposite tendency to the data weight reduction tendency after taking logarithm, or it had the same tendency to the origin data. This was introduced based on Gaussian function least square fitting to reduce noise sensitivity. In the process of solving Gaussian parameter, to improve the real-time performance, the solution process of inverse matrix was transferred to the solution process of simple equations because the computation of inverse matrix was time consuming. Gaussian function parameter, amplitude, center value and variance, were given with the fast calculation formulas. By applying these two methods to the practical fitting of 55Fe characteristic X-ray single spectrum peak, respectively, the results show that Gaussian function weighted least square fitting is more satisfactory. It indicates the proposed method can decrease the noise sensitivity and reduce the residual vector near the peak; in addition, the fitting precision is also improved. What's more, the real-time performance is improved by applying fast calculation formulas, which makes it possible to apply the proposed method to portable equipment efficiently.