This paper presents an improved droop control strategy for grid-connected inverter power stability and power quality under distorted with consideration of grid fluctuation and inter-harmonics. An instantaneous frequency without PLL and amplitude of capacitor voltage feed-forward control strategy is given to power stability control, meanwhile a grid current feedback control is given by an incomplete derivation with a high-pass filter, so that the harmonics and inter-harmonics current can be suppressed. These approaches can provide both good active and reactive power dynamic response under fluctuation of frequency, and rejection ability against harmonic and inter-harmonic voltage. Based on model of inverter, the proposed control strategies are designed in detail. Simulations and experiments are present to validate the effectiveness of proposed method.