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A modelling and stability analysis method of a virtual synchronous machine (VSM) is proposed in this study. VSM technology is used to solve the problems caused by the high permeability of distributed energy. Though VSM has inertia and damping characteristics, it is more prone to oscillate than a synchronous generator because of the characteristic and unexpected harmonics generated by power electronic elements. The traditional linear time invariant based model is difficult to analyse a time-variant system and cannot analyse harmonic coupling mechanism accurately. This study proposes a new model of a grid-connected VSM by using the harmonic state-space modelling approach, which is a typical linear time-varying periodic model and considers different harmonics of the system. The stability of the system is analysed by eigenvalues of system matrix, which is based on the harmonic state-space model. The theoretical modelling method and stability analysis are verified by direct time-domain simulation results.