The traditional Fixed Band Hysteresis Current Control (FB-HCC) though being widely used for the current control of grid integrated voltage source inverter (GI-VSI), has the drawback of variable switching frequency. To overcome this drawback, Complex Programmable Logic Device (CPLD) based switching scheme is proposed in this paper. The proposed method calls for a single reference wave and the control concept is to terminate the rising and falling inductor current (iL) either by the comparator or by the CPLD, based on the nature of its slope. Termination of the iL with steeper slope by the comparator ensures lower current ripple, whereas the CPLD ensures constant switching frequency (fsw). However, the iL obtained with the proposed logic has a DC offset, which is corrected by modifying the reference. The basic concept, switching logic, and reference correction are thoroughly detailed. MATLAB/Simulink results are included to verify the proposed concept. The constant frequency operation of the proposed method is also validated in a 2 kW, 230 V, 50 Hz GI-VSI prototype.