This paper offers an over-sampling method combined with zoom-FFT. The method is one of the methods which increases the resolving power of frequency in FFT analysis, and has the feature that it can choose arbitrary zoom ratio, i.e., arbitrary magnification of the resolving power of frequency. The results of investigation on the method are as follows : With the zoom ratio which make the fraction of normalized frequency some integer, the frequency component can be exactly extracted on its correct position; Smallest zoom ratio is sufficient for analysis; For Hamming window, the resolving power of two components is 2-normalized frequency under a zoom ratio smaller than 30; If the distance between two components is larger than 6-normalized frequency, Hanning window gives exact analysis with an amplitude error smaller than 0.1% and a phase error smaller than 0.1 degrees.