To reduce the ill- posedness of reconstruction for fluorescence molecular tomography (FMT), a reconstruction method combining adaptively iterative- shrinking permissible region strategy with subsection orthogonal matching pursuit algorithm is inspired by compressive sensing theory. The region of mesh nodes with higher fluorescent yield is chosen to iteratively shrink permissible region and make the objective function have a global optimal solution. In simulation experiments on digital mouse model, reconstruction results for single target and double targets demonstrate that greedy algorithm combining with shrink region strategy can not only significantly improve localization accuracy of fluorescent target and quantitative distribution of fluorescent yield, but also reduce dependence of algorithm on parameters choice. Physical simulation experiment further validates feasibility and stability of the proposed method in practical FMT applications.