In order to further solve the problems of traditional dual closed-loop algorithms of single-phase inverters such as poor load adaptability and large transient voltage fluctuations.In this paper, the error source essence of two kinds of single loop feedback is deduced theoretically and proposes a pulse-by-pulse control strategy based on fuzzy PID control in variational domain. The proposed algorithm compresses the traditional amplitude feedback to a sufficiently small interval, compared with the traditional method of giving the whole cycle effective value, the given value is the effective value corresponding to each small interval, that is, the interval effective value,the feedback value is the discrete rms of the sampling point, and use the variable universe fuzzy PID control to improve the robustness and control precision.Theoretical research shows that it can take into account the advantages of amplitude and instantaneous value feedback and improve the performance of the inverter device，at the same time, reduce the difficulty of loop parameter design. In order to verify the correctness of the algorithm, a 3kW test prototype is set up, and the experimental results show the effectiveness of the control method.