One of the major drawbacks of orthogonal frequency division multiplexing (OFDM) systems is their vulnerability to synchronization errors. To remedy the inter-carrier interference (ICI) effect caused by carrier frequency offset (CFO) estimation errors, this paper proposes a weighted linear parallel ICI cancellation (WLPICIC) equalizer. The optimal weights in the WLPICIC scheme are derived in closed-form expressions by maximizing the average signal-to-interference ratio (SIR) at the WLPICIC output of each sub-carrier. The simulation results show that the WLPICIC equalizer significantly improves the performance of OFDM systems with frequency estimation errors in both AWGN channels and frequency selective fading channels.