In this paper, a joint adaptive interference canceller (AIC) and maximum likelihood (ML) decoder scheme is proposed for a space-time coded DS-CDMA system with the difference between arrival times from transmit antennas. As the arrival time difference causes not only ISI and MAI, but also inter-antenna interference, performance degradation in the space-time coded DS-CDMA system is more severe than that of a regular DS-CDMA system with single transmit antenna. To mitigate the effect of the interference during space-time decoding, a joint algorithm for the proposed scheme merges adaptation process of the AIC into a ML decoding algorithm. Performance of the proposed scheme is evaluated for QPSK space-time trellis codes with two transmit antennas. It is shown that the proposed scheme achieves better performance than the conventional ML decoding scheme.