Gaussian functions are commonly used in different fields, many real signals can be modeled into such form. Research aiming to obtain a precise fitting result for these functions is very meaningful. This manuscript intends to introduce a new algorithm used to estimate the full parameters of the Gaussian-shaped function. It is basically a weighting method, starting from Caruana's method, while the selection of weighting factors is from the statistics view and based on the estimation of the confidence level for the samples. Tests designed for comparison with current similar methods have been conducted. The simulation results indicate a good performance for this new method, mainly in precision and robustness.