A method which describes the impulse response function of the fluorescence lifetime measurement system that based on a streak camera using Gaussian function is presented, and a mathematical model which is used to fit the fluorescence decay curves in time-domain is established. The data of the impulse response function of the time-domain fluorescence lifetime measurement system built using the Gaussian function are fit. The goodness of the fitting is greater than 0.995. The fluorescence lifetime of the standard fluorescent dye Rose Bengal is measured and the data using the mathematical model are fit. The average goodness of fitting is greater than 0.996 and the standard deviation of lifetime is only 1.7 ps. Experimental results show that the mathematical model is reliable and accurate in processing the time-domain signal obtained by fluorescence lifetime measurement system that is based on a streak camera. The method presented simplifies the deconvolution calculation, improves the precision of lifetime measurement and can be used to process time-domain signals obtained by other systems.