A new type of three‐phase quasi‐Z‐source indirect matrix converter (QZS‐IMC) is proposed in this paper. It uses a unique impedance network for achieving voltage‐boost capability and making the input current in continuous conduction mode (CCM) to eliminate the input filter. The complete modulation strategy is proposed to operate the QZS‐IMC. Meanwhile, a closed‐loop DC‐link peak voltage control strategy is proposed, and the DC‐link peak voltage is estimated by measuring both the input and capacitor voltages. With this proposed technique, a high‐performance output voltage control can be achieved with an excellent transient performance even if there are input voltage and load current variations. The controller is designed by using the small‐signal model. Vector control scheme of the induction motor is combined with the QZS‐IMC to achieve the motor drive. A QZS‐IMC prototype is built in laboratory, and experimental results verify the operating principle and theoretical analysis of the proposed converter. The simulation tests of QZS‐IMC based inductor motor drive are carried out to validate the proposed converter's application in motor drive. Copyright © 2013 John Wiley & Sons, Ltd.