This paper presents the implementation of indirect vector control of three phase Induction Motor using Hysteresis Band PWM current control and Synchronous Current Control in PSIM environment. In any machine drive system, current control directly influences both flux and torque developed directly. In Hysteresis current control method, actual current tracks the command current within a hysteresis band. There is no difficulty in current control tracking when CEMF is low, but at higher speeds, current controller gets saturated due to higher CEMF and hense becomes difficult to track due to which there will be a phase lag with respect to command current. All such problems are solved using Synchronous Current Control.