Discrete Fourier Transform (DFT) can calculate the phase and amplitude of the AC waveform directly from the sampled data. However, high performance microprocessor is inevitable to implement DFT into real time system, especially when conventional calculation algorithm is applied to high frequency sampling. Applying recursive algorithm to the DFT can drastically reduce the calculation amount. This paper studies about the phase detection error of DFT when recursive algorithm is applied. The proposed error correction method makes it possible to guarantee the correctness of detected phase, which is equivalent to the conventional DFT calculation algorithm. Also, this paper proposes the reset scheme of numerical error accumulation, which is unavoidable for the recursive algorithm applied DFT. The proposed method can guarantee high accuracy with minimum increment of calculation amount. The qualitative correctness estimated from the theoretical equations is confirmed through quantitative study by digital simulation.