Hybrid RF and baseband precoding can not only deal with low-scattering problem caused by severe signal attenuation of mmWave but also significantly reduce the power and cost of radio frequency (RF) chains and data converters in the massive MIMO transceiver. However, its baseband complexity is still very high for frequency-selective multi-carrier system such as orthogonal frequency division multiplexing (OFDM). Therefore, this paper proposes a computationally-efficient hybrid precoding algorithm for mmWave MIMO-OFDM systems. By decomposing the optimization of spectrum efficiency into many sub-optimization problems, we developed an iterative matrix-inversion-bypass algorithm to reduce the complexity. The baseband precoder was also designed to further reduce total complexity. The simulation and complexity analysis results showed that we can significantly reduce computational complexity for mmWave MIMO with negligible performance degradation compared to a state-of-the-art work in the literature.