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A new state-equation of the induction motor that is useful for transparent design of the vector control system is presented. In vector control, high performance of the current control is realized by the decoupling control. In case of the conventional state-equation and block diagram, the physical operation of the induction motor is difficult to understand from the block diagram. This is because, in the conventional block diagram, the dimension of the summing point has no physical meaning. To overcome this problem, a new state-equation and block diagram of induction motor will be proposed. In this proposed block diagram, all branches of the summing point have voltage dimension, and also the existence of couplings is clarified by matrix method. Consequently, the proposed equation enables easy understanding of the physical operation of the machine, and design of the decoupled controller become transparent and easy.