Fluorescence molecular tomography (FMT) allows the detection and quantification of various biological processes in small animals in vivo, which expands the horizons of pre-clinical research and drug development. Efficient three-dimensional (3D) reconstruction algorithm is the key to accurate localization and quantification of fluorescent target in FMT. In this paper, 3D reconstruction of FMT is regarded as a sparse signal recovery problem and the compressive sampling matching pursuit (CoSaMP) algorithm is adopted to obtain greedy recovery of fluorescent signals. Moreover, to reduce the modeling error, the simplified spherical harmonics approximation to the radiative transfer equation (RTE), more specifically SP₃, is utilized to describe light propagation in biological tissues. The performance of the proposed reconstruction method is thoroughly evaluated by simulations on a 3D digital mouse model by comparing it with three representative greedy methods including orthogonal matching pursuit (OMP), stagewise OMP (StOMP), and regularized OMP (ROMP). The CoSaMP combined with SP₃ shows an improvement in reconstruction accuracy and exhibits distinct advantages over the comparative algorithms in multiple targets resolving. Stability analysis suggests that CoSaMP is robust to noise and performs stably with reduction of measurements. The feasibility and reconstruction accuracy of the proposed method are further validated by phantom experimental data.