Single-carrier (SC) transmission with space-time block coded (STBC) transmit diversity can achieve good bit error rate (BER) performance. However, in a high mobility environment, the STBC codeword orthogonality is distorted and as consequence, the BER performance is degraded by the interference caused by the orthogonality distortion of STBC codeword. In this paper, we proposed a novel frequency-domain equalization (FDE) for SC-STBC transmit diversity in doubly selective fading channel. Multiple FDE weight matrices, each associated with a different code block, are jointly optimized based on the minimum mean square error (MMSE) criterion taking into account not only channel frequency variation but also channel time variation over the STBC codeword. Computer simulations confirm that the proposed robust FDE achieves BER performance superior to conventional FDE, which was designed based on the assumption of a quasi-static fading.