In this paper, a novel multiple-input multiple-output (MIMO) transmission scheme termed space-time block coded differential spatial modulation (STBC-DSM) is proposed. It employs the hybrid concept of differential spatial modulation (DSM) and space-time block coding (STBC) to exploit the diversity benefits of STBC without the channel state information (CSI). In the STBC-DSM scheme, information bits are conveyed via the antenna matrix (AM) indices, as well as STBC blocks. Specifically, a novel AM set is first designed such that the transmitter requires only sparse (one or two) frequency radio (RF) chains. Then, the proposed STBC-DSM scheme is extended to the large-scale MIMO scenarios, and a low-complexity near-optimal detection algorithm is developed. Finally, an upper bound for the average bit error probability of the proposed scheme is derived. Both analytical and simulation results have shown that the proposed scheme is capable of achieving considerable performance gains over the existing DSM and differential Alamouti schemes.