The development of fluorescence lifetime analysis method suitable for low photon count is of great significance for the evelopment and application of fast fluorescence lifetime imaging microscopy (FLIM). In this paper, we consider the fluorescence lifetime analysis, inspired by the compression sensing algorithm in high-density single molecule localization microscopy, as a sparse inverse problem, and we propose an alternating descent conditional gradient (ADCG) based method for fluorescence lifetime analysis. Through the analysis of simulation data and experimental data, we demonstrate that the ADCG-FLIM algorithm can be appropriately implemented to analyze fluorescence lifetime even in the case of low photon count, thereby benefiting the development and application of live cell fast FLIM.