In this paper, we propose a transmit multi-block frequency-domain equalization (MB-FDE) for frequency-domain space-time block coded joint transmit/receive diversity (FD-STBC-JTRD). Noting that a STBC codeword consists of multiple coded blocks, the transmit MB-FDE uses the multiple transmit FDE weight matrices, each associated with each coded block. Both single-carrier (SC) transmission and orthogonal frequency-division multiplexing (OFDM) transmission are considered. For SC transmission, the transmit MB-FDE weight matrices are jointly optimized so as to minimize the mean square error (MSE) between the transmit signal before STBC encoding and the received signal after STBC decoding. For OFDM transmission, they are jointly optimized so as to maximize the received signal-to-noise power ratio (SNR) after STBC decoding. We show by theoretical analysis that the proposed transmit MB-FDE can achieve 1/R_STBC times higher received SNR than the conventional transmit single-block FDE (SB-FDE), where R_STBC represents the code rate of STBC. It is confirmed by computer simulation that, when more than 2 receive antennas are used, MB-FDE can always achieve better BER performance than SB-FDE irrespective of the number of transmit antennas, and the channel frequency-selectivity.