The power quality of virtual synchronous generator (VSG) inevitably deteriorates in the presence of local nonlinear loads and distorted grid. In this paper, the conflict involved in the simultaneous elimination of distortion for both the inverter local load voltage and the grid exchanged current is first described. A unified control structure is presented that enables a tunable tradeoff between the two constrained harmonic sources. Then, a hybrid harmonic suppression scheme is proposed to enable the further improvement of the adaptability of VSG, which mainly consists of a local voltage harmonic control loop and an adaptive grid current-controlled loop. The local voltage harmonic control loop aims to scale down the inverter output impedance via a negative feedback loop, while the grid current-controlled compensator is intended to counteract the adverse effects from a weak grid via an additional voltage, which leads to substantially lower total harmonic distortion for both the local load voltage and the grid current at the same time. Small-signal modelling is performed to investigate the system stability and its robustness to parameter perturbations. The effectiveness of the proposed methodology is verified using hardware-in-the-loop simulations.