Peak-to-average power ratio (PAPR) reduction methods for orthogonal frequency division multiplexing (OFDM) systems commonly use four times oversampling for the discrete-time OFDM signal to approximate the peak of the continuous-time OFDM signal. However, the four times oversampling process increases the computational complexity. In this paper, we propose a new low-complexity method to efficiently estimate the PAPR value of the OFDM signal. The proposed scheme uses an interpolator to find the peak of the four times oversampled OFDM signal around some searched samples of the original discrete-time OFDM signal using oversampling with a factor lower than four. Some criteria are derived to determine the interpolation filter length and the threshold of sample power for the search process. As compared to the method with four times oversampling, the proposed PAPR estimation scheme achieves close performance with only about half of the computational complexity. It is also shown that the proposed approach can easily be combined with the selected mapping method for PAPR reduction, where the complexity is significantly reduced but the performance is degraded only slightly.