Maximum likelihood detection with QR decomposition and M-algorithm (QRM-MLD) is one of the detection methods in multiple-input multiple-output (MIMO) multiplexing. We recently proposed an iterative QRM-MLD with decision directed channel estimation and showed that better transmission performance can be obtained compared to that with conventional pilot assisted channel estimation. In this paper, to further improve the transmission performance while keeping computational complexity low, we modify previously proposed iterative QRM-MLD by applying cyclic redundancy check (CRC) coding. In the proposed method, transmitted signals are ranked according to their CRC check results and signal-to-interference plus noise power ratio (SINR), before performing modified QRM-MLD. The number of iterations and that of surviving symbol replica candidates in iterative channel estimation/signal detection are adaptively controlled by CRC check results. Thus, the computational complexity of the proposed method can be kept low. Computer simulation results show that the loss in the average received signal energy per bit-to-noise power spectrum density ratio Eb/N0 required for the average packet error rate (PER) of 10-2 is approximately 0.5 dB from full MLD with ideal channel estimation for QPSK modulation