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For uplink multi-carrier code-division multiple access (MC-CDMA) systems, we propose a multiuser detector that is robust to a small residual frequency offset existing after frequency offset estimation and compensation. In this paper, when the residual frequency offset is normalized by subcarrier spacing, it is called a normalized residual frequency offset (NRFO). In the proposed scheme, we first derive a lower bound of the signal-to-interference plus noise ratio (SINR) of the desired user when the NRFO of the desired user is bounded by a small value and the value is known to the receiver. We then design a detection filter to maximize the SINR lower bound. Simulation results show that the proposed scheme has better SINR and bit error rate (BER) performances in a high signal-to-noise ratio (SNR) region than a conventional minimum mean square error (MMSE) receiver that ignores the NRFO.