In grid-connected mode, current-controlled battery energy storage systems (BESS) face the issues of harmonic caused by nonlinear loads and interactive instability under weak grids. Firstly, the mechanisms of mid-frequency oscillations (MFO) and mid-frequency harmonics (MFH) are revealed by the impedance network theory and the circuit principle. Because harmonic currents of nonlinear loads tend to interact with the mid-frequency impedance of BESS to produce harmonic voltage drops, the grid is susceptible to MFH. Worse still, the grid-connected system based on BESS tends to exhibit negative damping characteristics in the mid-frequency band as the grid stiffness decreases, which triggers MFO. Aiming at the above problems, this paper proposes a quasi-harmonic voltage compensation control strategy without any harmonic extractor and provides a detailed parameter design rule. The proposed control strategy can effectively suppress MFO by enhancing the damping between BESS and weak grids. Meanwhile, the disturbance resistance of BESS to nonlinear loads is significantly improved because the impedance magnitude of BESS in the mid-frequency band is obviously reduced. Finally, the effectiveness of the proposed strategy is verified by simulation and experiment.