In this paper, discrete current control of voltage source inverters is proposed. As a current control scheme, the constant switching frequency predictive current control is adopted and implemented with DSP microprocessor system. In particular, the proposed method is for the compensation of the control lagging due to calculation delays in the microprocessor controller. In controlling the current, the inverter output voltage saturation problem is inevitable and usually affects the current control performance. So, the saturation boundary condition of the inverter output voltage and its effects on the current controal performance of the proposed current control scheme are investigated with experiment. Finally, the proposed scheme is applied to the active power filter system and some results are described for validation.