The large-scale system matrix generated during the reconstruction procedure of multiple excitation points based on fluorescence molecular tomography (FMT) leads to the high computational complexity and long reconstruction time. In order to shorten the reconstruction time and ensure its accuracy, based on the theory of artificial neural network (ANN), we propose a fast reconstruction method for FMT by reducing the dimension of system matrix in this paper. Specifically, the dimension reduction tool is the autoencoder (AE), which is a famous ANN architecture, and during the training of AE, the input matrix data consists of system matrix and surface fluorescence measurement data, then the representation of the previous matrix in the lower dimensional space is obtained by utilizing encoder part of AE. To test the performance of our method, a series numerical simulation experiments are devised, including non-heterogeneous cylinder and digital mouse experiments. Experimental results demonstrate that our method can effectively shorten the time of FMT reconstruction as well as obtain a good reconstruction accuracy.