The grid voltage modulated direct power control (GVM-DPC) for grid-connected voltage source inverters has been introduced so that it can overcome the poor steady-state performance of the DPC. However, it was designed for a non-distorted grid voltage. In this paper, the GVM-DPC is modified to overcome a distorted grid voltage(e.g., fifth and seventh harmonics). First, a band pass filter is applied to extract the fundamental component of the voltage so as to build a model for the implementation of the GVM-DPC method. Next, a sliding mode control(SMC) is designed to handlethe terms of the harmonic in order to minimize the total harmonic distortion(THD) of the output currents. Simulations and experimental results are presented to verify the effectiveness of the proposed SMC with GVM-DPC control strategy. It is shown that although the performance of real and reactive powers are sacrificed, the THD of the current is significantly reduced.