This paper presents a control strategy of induction motor (IM) driven by a matrix converter (MC) operating in boost mode. In this paper, indirect matrix converter (IMC) of the various MC topologies is used to the energy conversion system. The IMC is an AC/AC power conversion system and it does not have a DC-link energy storage element as bulky capacitor or inductor. For this reason, the IMC has many advantages that compact size, low weight and durability. Furthermore, it features full four-quadrant operation and sinusoidal input-output currents. However the IMC usually operated with maximum voltage transfer ratio of 0.866, which is an inherent restriction. In order to increase the voltage transfer ratio, the novel structure of the IMC that reverses the direction of power flow is adopted. This structure operates boost mode without auxiliary elements or circuits. Finally, the effectiveness of the proposed method is confirmed by simulation results.