Aiming to co-antenna interference and multipath interference in the downlink multiple input multiple output orthogonal frequency division multiple multiplexing (MIMO-OFDM) asynchronous communication system, a low complexity iterative equalization algorithm based on precoding matrix is proposed. At the transmitter, the algorithm utilizes precoding matrix to spread the symbols over all the subcarriers, which relieve the influence of deep fading in part of the subcarriers. At the receiver, the algorithm adopts Soft input soft output(SISO) interference elimination algorithm based on the minimum mean square error sorted QR decomposition (MMSE-SQRD) to avoid the complexity of solving inverse matrix, which is always involved in the traditional parallel soft interference elimination algorithm based on minimum mean square error(MMSE)equalization. Utilizing a sorted QR decomposition of the channel matrix, on the other hand, the algorithm has the priority for detection transmission symbol with maximum noise-signal ratio (SNR) to improve detection accuracy. Furthermore, the error of reconstructed signals is spread by the precoding matrix, which decreases the error propagation in iteration processing. Simulation results show that the performance of the proposed algorithm is improved compared with the existing iterative interference cancellation algorithm, that is, when the system is equipped with 2 transmitters and 2 receivers and the Bit error rate is 10-3, the performance of the system is improved about 2dB.