A new adaptive iterative block-delayed partitioned Viterbi algorithm (AIBD-PVA) receiver for the MIMO frequency-selective fading channel is proposed. In the classic PVA, tentative decisions are used for the feedback between the trellis detectors of each transmit antenna. The block-delayed PVA uses more reliable temporary decisions in the feedback loop. The proposed algorithm adapts the number of iterations used to improve the reliability of the feedback decisions depending on the detection conditions, thus resulting in an improved BER performance without adding unnecessary complexity. It is observed that MIMO systems with higher numbers of antennas have a more remarkable BER performance improvement, since they rely more on the feedback between the trellis detectors.