The power system frequency plays an important role in monitoring and controlling the power system. The frequency can be measured through discrete Fourier transform (DFT) coefficients of its positive fundamental frequency. The accuracy of the frequency estimate is severely affected by noise in the power system signal and the leakage effect of the negative fundamental frequency in DFT. This paper proposes a DFT-based frequency estimation algorithm to cope with the noise as well as the leakage effect. In this algorithm, two suitable digital filters are introduced to reduce efficiently frequency estimate error due to the noise. These filters are designed to use a digital bandpass filter and a second-degree integrator. The effectiveness of the proposed algorithm in reduction of frequency estimate error is verified through simulations on noise, harmonics and frequency deviation.