A simple DFT-based noise variance estimator for orthogonal frequency division multiplexing access (OFDMA) systems is proposed. The conventional DFT-based estimator differentiates the channel impulse response and noise in the time domain. However, for partial frequency response, its time domain signal will leak to all taps due to the windowing effect. The noise and channel leakage power become mixed. In order to accurately derive the noise power, we propose a novel symmetric extension method to reduce the channel leakage power. This method is based on the improved signal continuity at the boundaries introduced by symmetric extension. Numerical results show that the normalized mean square error (NMSE) of our proposed method is significantly lower than that of the conventional DFT method.