For orthogonal frequency-division multiplexing (OFDM) systems equipped with multiple receive antennas, conventional pre-discrete Fourier transform (DFT) combining cannot balance the signal-to-noise ratio (SNR) performance of all subcarriers. This degrades the whole system performance. In this paper, we propose the use of the max-min fair criterion for pre-DFT combining to solve the problem. Semidefinite relaxation (SDR) is employed to approximate the solution. We also present a simple way to effectively reduce the amount of computation without sacrificing much of the performance. Simulation results show that, for both uncoded and coded OFDM systems, the proposed max-min fair pre-DFT combining solved via SDR can outperform conventional pre-DFT combining under various multipath channel environments with affordable computational complexity.