To improve the quality of wireless communication, transmit/receive diversity techniques in multiple-input multiple-output (MIMO) system have been investigated vigorously. In this paper, we consider an asymmetric MIMO orthogonal frequency division multiplexing (MIMO-OFDM) system, in which the number of transmit antennas is larger than that of receive antennas. In this system, there is a need to achieve the high quality of communication in both low and high mobility scenarios by a single transmit diversity scheme. Recently, as for the advanced diversity schemes based on space time block coding (STBC)/space frequency block coding (SFBC), STBC/STBC-phase shift diversity (PSD) and SFBC-frequency switched transmit diversity (FSTD) have been proposed. However, in these schemes, it is possible that time diversity gain can not be sufficiently obtained especially in the low mobility scenario. Therefore, in this paper, the joint use of grouped phase rotation in time/frequency domain and STBC (GPR-STBC) is proposed to get the larger channel coding gains than other schemes. In this paper, we evaluate the average bit error rate (BER) performance by computer simulation in a comparison with the conventional transmit diversity schemes and discuss the relationship from the viewpoints of BER performance and computational complexity.