The introduction of space-time block code (STBC) can efficiently increase the diversity of original spatial modulation (SM). However, the spectral efficiency of STBC will be reduced gradually with the increase of the transmit antennas. In this contribution, we conceive a novel quasi-orthogonal space-time block coded spatial modulation (QOSTBC-SM) design for multiple-input and multiple-out (MIMO) transmission by reaping their respective benefits, while improving the spectral efficiency compared to conventional space-time block coded spatial modulation (STBC-SM). More specifically, in the proposed QOSTBC-SM structure, the information bits are conveyed via the active antenna index, as well as the QOSTBC blocks at the transmitter, while at the receiver, a low-complexity detection scheme is proposed. Furthermore, a closed-form union bound of the bit error rate (BER) is also quantified by theoretical derivation. Finally, our simulation results demonstrate that QOSTBC-SM is capable of outperforming the conventional counterpart as STBC-SM with higher spectral efficiency.