Tri-electrode plasma actuator (TED-PA), which has an additional electrode with DC high voltage, can induce stronger jet than that of conventional two-electrode plasma actuator. However, the engineering application is limited due to the arc discharge occurrence with increasing the applied voltage amplitude. In this study, we aim to enhance the EHD force generation in the TED-PA without increasing the voltage amplitude by utilizing the EHD force generation around the DC electrode effectively. First, we conduct a plasma simulation to investigate the mechanism of the EHD force generation. As a result, the positive EHD force generation around the DC electrode is due to the drift motion of positive ions generated by DC discharge around the DC electrode, and enhanced by electron supply from negative discharge around the AC electrode which appears in the negative-going voltage phase of the AC voltage. On the other hand, the drift motion of negative ions generated by the negative discharge generates the negative EHD force not only around the AC electrode but also around the DC electrode. Second, we propose to apply a waveform voltage with negative-going voltage phase of 5 % and the phase with negative peak voltage of 90 % to the AC electrode based on the mechanism. The simulation results indicate that the proposed waveform can significantly enhance the EHD force generation in the TED-PA.