Abstract: The electromagnetic fields in multi-scale complex electronic systems are difficult to compute with conventional methods in computational electromagnetics. Generalized transition matrix (GTM) method has been proposed based on domain decomposition method (DDM) and Huygens' equivalence principle, in which a complex system is divided into many sub-blocks. Every sub-block is analyzed independently to get its electromagnetic characteristics. By taking into account mutual couplings among all blocks, the electromagnetic field in the whole system can be calculated. According to generalized transition matrix method, a multi-scale system is turned into an equivalent system consisting of sub-blocks with roughly the same scale. It provides flexible solutions to analyze the electromagnetic scattering problems involved in complex systems such as scatterers with hybrid structures, inhomogeneous isotropic media, and large-scale phased antennas. Numerical examples of applying GTM to analyzing the electromagnetic properties of a chiral scatterer, open-ended cavity and a vivaldi antenna array are presented, in which the unknowns have been reduced to about 1/10 of their original ones, while the numerical results with GTM still agree very well with those obtained with method of moment (MoM) directly. The target scattering properties can be expressed concisely by the generalized transition matrix. Compared with traditional methods of moment, the number of basis function is greatly reduced via GTM, hence improving the computational efficiency.