A blind algorithm is proposed in order to compensate for the phase noise resulting from imperfect oscillators in orthogonal frequency-division multiplexing (OFDM) systems over constant modulus modulation. In the proposed algorithm, one received OFDM symbol is partitioned into subblocks in the time domain and the phase noise over each subblock is approximated as its time-average. Under the approximation, the squared magnitude of the channel gain multiplied by the data symbol at each subcarrier is shown to be expressed in terms of these time-averages and the discrete Fourier transform (DFT) coefficients of the received samples at each subblock with zero padding. Based on the relation, the proposed algorithm compensates for the phase noise without pilot symbols. Numerical results show that the proposed algorithm outperforms conventional algorithms as well as it requires lower computational complexity.