We have introduced a method for the calculation of electron transport in a multi-terminal quantum system based on the recursive Green's function technique. The corresponding transport equation is presented by scattering matrix, which is exp ressed by Green's function. Using this method, the multi-terminal device can be simplified as a standard two-terminal device, which is convenient in treating th e mesoscopic device. It is found that the transmission and reflection probabilit ies of the two multi-terminal quantum systems show complex spectra. The results show that the special node can destroy the symmetrical conductance spectra, and there is a new conductance peak in the low-energy region. This method can also b e applied to the study of electron transport of complex mesoscopic structures.