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The paper proposes a new CFO (carrier frequency-offset) estimation method for OFDM systems. This method uses scattered pilots to estimate both integer and fractional CFO, which are usually estimated by continual pilots. Since scattered pilots are usually used to estimate the CFR (channel frequency response), using them at the same time, to estimate frequency-offset does not bring about additional cost for the system. Thus, subchannels applied to transmit the continual pilots, are saved for useful data, which increases the spectral efficiency. Moreover, performances of estimating CFO by both scattered and continual pilots are compared and analyzed in both AWGN and multipath fading channels. Theoretical analysis and simulation results show that for both integer and fractional CFO estimation, the performance of the scattered pilots-based algorithm is as good as that of continual pilots-based algorithms or acceptable for practical application.