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If there is a frequency offset in the local oscillator circuit in QPSK demodulation, the BER is degraded. Previously, methods for estimating this frequency offset have been proposed. However, few techniques that have been studied can estimate this offset in an environment with a large frequency offset or noise. A digital adaptive IIR notch filter is effective for estimation of a large frequency offset in an environment with noise. However, the noise is colored in the receiver due to the IF band BPF inserted in order to suppress out-of-band noise. Therefore, the converged value has a bias error with respect to the target value. The method proposed in this paper is based on the fact that the phase of the digital IIR-BPF is zero at the center frequency of the amplitude characteristic. This characteristic is used for control by applying a negative feedback to the digital IIR-BPF coefficients. Then, no bias error is generated because the noise in the in-phase channel and that of the quadrature channel in QPSK are uncorrelated. Further, the proposed method does not drift but maintains the present status due to the uncorrelated character described above, even in the case of channel disconnection such as shadowing. Therefore, this is a frequency offset estimation method suitable for mobile communications. As a result of evaluation of the proposed method in terms of the BER in a white Gaussian noise channel, it is confirmed that the proposed method provides a BER lower than that of the conventional digital adaptive IIR notch filter. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(9): 1–12, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10089 [ABSTRACT FROM AUTHOR]