In order to fit the spectral overlapping peaks and terahertz time-domain curves, a Gaussian fitting algorithm that dynamically increases the Gaussian function is designed in this paper. First, use the first derivative of the denoising spectral data to roughly search the position of each Gaussian peak, and then initialize the multi-Gaussian function according to the position of the Gaussian peak. Then, the mean square error between the spectral data and the multi-Gaussian function is used as the loss function, and the gradient descent method is used to find the multi-Gaussian function when the loss function is the smallest. Finally, for the spectral overlapping peaks without obvious peaks and the terahertz time-domain curves with negative values, the dynamic multi-Gaussian function model is used to analyze overlapping Gaussian peaks or fitting curves. Calculation results show that the algorithm can dynamically add multi-Gaussian functions according to the requirements of fitting accuracy, and automatically search for the position of Gaussian peaks, and the effect of fitting spectral overlapping peaks and terahertz time-domain curves is better.