A generic small-signal model of modular multilevel converter (MMC) based DC grid is established and a DC virtual impedance damping control to suppress the resonance and instability is proposed. The averaged-value model (AVM) of MMC is employed to derive the Thévenin equivalent model of the converter from its DC side using the power-balancing principle considering the dynamics of phase-locked loop (PLL) of the interconnected ac system. The single section π-typed line model is selected to develop the nodal admittance equations of the DC network in s domain. The stability criterion of the DC grid is given after establishing the generic linearization model. The key factors affecting the DC grid's stability are identified using the root locus method and participation factors analysis. The parameters and the performances of the damping controller are designed and studied. Electromagnetic transient simulation model and RT-LAB real-time simulation are used to validate that the proposed damping control can suppress the instability of the DC grid and improve its operating performance.