Recently fluorescence tomography is developed as a promising way for non-invasive molecular-based imaging, especially for small animals. Based on a certain forward model with known optical properties, the distribution of fluorescence parameter could be estimated by proper inversion techniques. In this work, a novel fast inversion algorithm is applied to a linear scheme, which is generated by solving the diffusion equations with finite element method. The proposed reconstruction algorithm consists of a pre-iteration step executed off-line and an on-line post-processing step. In the off-line step the approximated value of generalized inverse is obtained by a iteration method of two-order expression. In the on-line step when the updated measurements come, a rough distribution of the required fluorescence parameter is firstly estimated by a matrix-vector multiplication, and then several steps of Landweber iteration are applied, which reduces the influence of the noisy measurements and integrates a priori knowledge about the unknown values. Numerical simulations of 2-D geometry model show that the algorithm could well estimate the spatial distribution of the fluorescent yield.