Replacing the capacitor current with the derivative of its voltage in the active damping (AD) loop of a grid-connected inverter (GCI) can save cost and gain popularity. However, the first-order differentiator (FOD) based AD solution cannot address the negative conductance region around the Nyquist frequency. In this paper, a new PD design method is proposed to tune the output admittance of the FOD-AD-based GCI system to be passive at full frequency. Meanwhile, Pareto-optimal technology is applied in the PD design approach to ensure that PD parameters are Pareto-optimal in terms of efficiency and passivity. A 4 MW FOD-AD-based GCI design example is provided to compare performance with other state-of-the-art design methods. Finally, the effectiveness of the proposed approach in stabilizing the GCI is verified on a scaled-down 1.4 kW experimental prototype.