We present a low-complexity maximum likelihood (ML) detector for a coded double space-time transmit diversity-orthogonal frequency division multiplexing (DSTTD-OFDM) system. The proposed ML detector exploits properties of two permuted equivalent channel matrices and multiple decision-feedback (DF) detections. This can reduce computational efforts from O(|A|⁴) to O(2|A|²) with maintaining ML performance, where |A| is the modulation order. Numerical results shows that the proposed ML detector obtains ML performance and requires remarkably lower computational loads compared with the conventional ML detector.