We analyze the limitation of the fast Fourier transform (FFT) method applied to the spectrum analysis of the optical frequency domain reflectometry (OFDR). The shortcomings of the fast Fourier transform-segmented Chirp-Z transform (FFT-SCZT) algorithm are discussed. Based on an improved genetic algorithm (IGA) and Zoom FFT (ZFFT), a fast and high-resolution spectrum analysis algorithm, FFT-IGA-ZFFT algorithm, is proposed. The computation procedures of the proposed algorithm are described and its time complexity is deduced. The experimental result shows that the FFT algorithm costs 3.130 s, the FFT-SCZT algorithm costs 1.993 s, and the FFT-IGA-ZFFT algorithm costs 0.525 s when 107 OFDR sampling data is processed in the same computing platform and with the same resolution. The FFT-IGA-ZFFT algorithm is outstanding in term of processing speed.