Anti-islanding detection is a mandatory function of grid-connected inverters. This paper proposes a novel active frequency drift (AFD) islanding detection method to solve the problems of the classic AFD method, such as longer detection time and larger non-detection zone (NDZ). In the proposed AFD method, an approximating cosine disturbance current waveform is injected into the original reference current waveform, so that there is less side influence on power quality when the reactive power generated by reference current waveform equals. This paper analyzes the relationship between the total harmonic distortion (THD) and Q/P and the distribution of NDZ in the proposed method through the value decomposition of the proposed reference current waveform, and compares the new method with the classic AFD method. The simulation results show the proposed method has shorter detection time, smaller NDZ and less influence on power quality.