The all-phase fast Fourier transform (apFFT) is proposed as a digital demodulation algorithm in place of the fast Fourier transform (FFT) for orthogonal frequency division multiplexing (OFDM) based multiple-input multiple-output (MIMO) communication systems. The amplitude spectrum of apFFT-demodulated symbols is the square of that of the FFT, which helps reduce the Gaussian noise to a great extent. Moreover, the phases of apFFT symbols are not affected by the frequency shift between the transmitter and receiver oscillators. These properties particularly appeal to MIMO systems over frequency-selective fading channels. The proposed MIMO-OFDM system employing the apFFT is validated using the spatial channel model (SCM) proposed by the third generation partnership project (3GPP). The simulation results demonstrate that the performance of the proposed system after compensating for the rate loss due to zero bits inserted in the space-frequency OFDM (SF-OFDM) coding scheme, still considerably outperforms the conventional system over 3GPP SCM channels, especially under poor channel conditions.