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The bifurcation behavior of a digitally controlled H-bridge grid-connected inverter is studied in this paper. The discrete-time model of this time-varying system is derived for inherent time delay in a digitally controlled system. Theoretical analyses indicate that only Hopf bifurcation can take place when the system loses its stability. The analytical expression of oscillation frequency is also derived in this paper. Moreover, the stability and instability boundaries for all switching cycles within a line cycle are described by analytical expressions. Finally, the theoretical results are verified by numerical simulations, circuit simulations and experimental measurements. These aforementioned conclusions provide an insight into the design process of the inverter system in terms of stability behavior and instability phenomenon.