Binary phase shift keying (BPSK) orthogonal frequency division multiplexing (OFDM) has been adopted in the fourth-generation wireless communications. However, the real-valued property of BPSK-OFDM signals has not yet been utilized for channel equalization. In this work, this property is employed to develop a new equalizer based on the minimum mean square error (MMSE) criterion, leading to considerable enhancement in signal detection. In particular, the proposed equalizer is able to achieve 3 dB improvement over the existing MMSE equalizer in large signal-to-noise ratio region, and more robust against channel estimation errors. Moreover, successive detection technique employed in the devised method is able to make use of diversity in time-varying channels, resulting in further performance enhancement. Additionally, the computational complexity of the proposed approach is analyzed. Simulation results are included to illustrate its performance superiority and computational attractiveness.