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Linear precoding plays an important role in the spatial multiplexing multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems which are considered one of the primary candidates for the physical-layer techniques in the next-generation wireless communication systems. It requires the channel state information (CSI) at the transmitter to adapt the transmitted signal to the channel conditions. In most communication systems, the CSI is estimated at the receiver and fed back to the transmitter. However, the error performance in a precoded MIMO-OFDM system is significantly degraded due to the long feedback delay that causes the outdated CSI at the transmitter. In this paper, a novel approach using multi-block linear channel prediction is proposed to combat the feedback delay in a limited feedback precoded spatial multiplexing MIMO-OFDM system. The time-varying channel is modeled by autoregressive (AR) process, whose coefficients are obtained by linear minimum mean square error (MMSE) method. To increase prediction range, block-based channel samples are used to establish the AR model, and multiple blocks are employed to iteratively predict the CSI. Simulation results show that the performance degradation caused by large feedback delay can well be mitigated.