This paper introduces a Discrete Fourier Transform (DFT)-based algorithm to extract the Electric Network Frequency (ENF) information from an audio recording for use in audio authentication. The basic idea of the proposed algorithm is to calculate the specific spectral lines by DFT in the frequency domain at the desired frequency point instead of throughout the entire frequency band. Then a binary search technique is employed to search the next desired frequency bin to repeat the spectral line calculation until the hidden ENF information is extracted. The purpose is to improve the accuracy and precision of conventional ENF extraction methods and also to enhance the calculation efficiency. Both simulated audio signals with different signal-to-noise ratios (SNRs) and actual audio recordings are studied to verify the performance of the proposed algorithm. Two error-evaluation criteria, frequency offset and frequency bias, are defined to evaluate the algorithm performance on accuracy and precision. The test results and the error evaluation prove the validation and demonstrate the improvement of the proposed algorithm.