As extensive renewable energy-based distributed generators (DGs) are integrated into the microgrids (MGs), system inertia drops sharply, posing enormous challenges to power quality. Inspired by the conventional synchronous generator(SG), a novel control structure called virtual synchronous generator (VSG) is proposed to provide ancillary rotor regulation. Moreover, existing distributed control algorithms highly rely on explicit state sharing, which exposes MGs to potential privacy leakage threats. To this end, a distributed self-triggered privacy-preserving secondary control of VSG-based AC MGs is proposed to achieve control objectives while protecting the initial and real-time values. First, VSG is modeled by mimicking the operation of SG to provide inertial and damping support for MGs. Considering the nonlinear dynamic characteristics of VSGs, a novel VSG-integrated distributed secondary control strategy with inertial-support is established to achieve control objectives. Moreover, we present a more comprehensive definition of privacy preservation. Next, a Paillier encryption-based privacy-preserving algorithm is innovatively developed to tackle the potential data disclosure problems that need to be faced when performing continuous information interaction. Further, to attenuate the effect of extra encryption costs, we propose a self-triggered mechanism to significantly reduce 86% communication resources. Finally, the superior performance of the proposed strategy is testified by numerical case studies.