Fluorescence molecular tomography (FMT) is a fast-developing optical imaging modality that has great potential in early diagnosis of disease and drugs development. However, reconstruction algorithms have to address a highly ill-posed problem to fulfill 3D reconstruction in FMT. In this contribution, we propose an efficient iterative algorithm to solve the large-scale reconstruction problem, in which the sparsity of fluorescent targets is taken as useful a priori information in designing the reconstruction algorithm. In the implementation, a fast sparse approximation scheme combined with a stage-wise learning strategy enable the algorithm to deal with the ill-posed inverse problem at reduced computational costs. We validate the proposed fast iterative method with numerical simulation on a digital mouse model. Experimental results demonstrate that our method is robust for different finite element meshes and different Poisson noise levels.