In this paper, the most widely used adaptive hysteresis band current controller is proposed for Voltage Source Inverter used in Uninterrupted Power Supply (UPS) to eliminate harmonics in output voltage and current. By comparing with other controllers, the Hysteresis band (HB) is used in this controller which makes the current error back to zero by recursively stepping through successive voltage levels. The adaptive hysteresis band current controller changes the hysteresis bandwidth according to switching frequency, supply voltage, dc capacitor voltage and slope of the reference compensator current wave. The output result of an adaptive hysteresis current controller is compared with the fixed hysteresis current controller and also with the Pulse Width Modulated (PWM) controller for the same Voltage Source Inverter. Simulations have been carried out through MA TLAB Simulink Power System Toolbox in MA TLAB 2010a.