A general method to calculate various transmission coefficients for two-terminal systems based on tight-binding models with fluctuating on-site energies in the scattering region was presented, then, a two-dimension H-shaped quantum dot array of four-terminal system based on real-space lattice models was presented. Problem of the quantum transport in a four-terminal system can be reformulated into a problem of the quantum transport in an effective two-terminal system and then be treated using a standard two-terminal method. By exploiting real-space Green’s functions, the transmission coefficients of four-terminal quantum dot array were calculated, and the problem of quantum transport was treated.