To complete the sparse sampling of linear frequency modulation (LFM) signals and estimate the parameters, the authors proposed an improved finite rate of innovation (FRI) system to achieve the goal. First the authors build a mathematical model based on the Z‐transform, then they input the LFM signal into the modified FRI system and process the output of the system based on this mathematical model, which enables the estimation of the parameters of the LFM signal using only four sampling points. The error of the final experimental results can be controlled within 3%, which greatly improves the efficiency of LFM signal parameter estimation.