This paper proposes two control strategies for the bidirectional Z-source inverters (BZSI) supplied by batteries for electric vehicle applications. The first control strategy utilizes the indirect field-oriented control (IFOC) method to control the induction motor speed. The proposed speed control strategy is able to control the motor speed from zero to the rated speed with the rated load torque in both motoring and regenerative braking modes. The IFOC is based on PWM voltage modulation with voltage decoupling compensation to insert the shoot-through state into the switching signals using the simple boost shoot-through control method. The parameters of the four PI controllers in the IFOC technique are designed based on the required dynamic specifications. The second control strategy uses a proportional plus resonance (PR) controller in the synchronous reference frame to control the AC current for connecting the BZSI to the grid during the battery charging/discharging mode. In both control strategies, a dual loop controller is proposed to control the capacitor voltage of the BZSI. This controller is designed based on a small signal model of the BZSI using a bode diagram. MATLAB simulations and experimental results verify the validity of the proposed control strategies during motoring, regenerative braking and grid connection operations.