This paper introduces two different types of AC current control methods for an indirect vector controlled induction motor using a matrix converter. The proposed methods combine the advantages of matrix converters with the advantages of the indirect vector AC current control methods. The first proposed method explains the basic idea of the hysteresis current control method for matrix converters and shows its capability and stability in comparison to the conventional method usually used for VSI. With the aid of the special configuration of the matrix converter, we also propose another current method which is modified from the first one in order to reduce both current ripple and torque ripple. Simulation results have verified the feasibility and the effectiveness of the proposed methods.