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This paper proposes a simple, yet effective generalized sidelobe canceller (GSC)-based Capon multiuser receiver for the Alamouti space-time block coded (STBC) multiple-input multiple-output code-division multiple-access (MIMO CDMA) systems. The new receiver makes full use of the space diversity provided by the antenna array and the time diversity provided by the decision feedback (DF) from the outputs of both of GSCs employed along with the transmit diversity induced in the Alamouti STBC to render superior performance. With an ingenious DF scheme, refer to as the the cross DF (CDF), the desired signals will be blocked more thoroughly after the blocking matrix so that the interference suppression capability can be further enhanced. Performance analysis is also provided to show that that the minimum mean squared error (MMSE) of the receiver using the CDF is indeed lower than those with or without the classical DF scheme. Conducted simulations show that the new receiver can not only provide superior performance compared with previous works, but it can also render faster convergence characteristics.