A design of closed-loop grouped space-time block codes (G-STBCs) including encoding, decoding and codeword selection is proposed for the downlink over Rayleigh flat-fading channels. In particular, at the transmitter, the antenna array is partitioned into a number of groups, each of which is encoded based on the orthogonal STBC (O-STBC). At the receiver, by exploiting the algebraic structure of orthogonal codes, a low-complexity, in recursion form, group-wise ordered successive interference cancellation (OSIC) detector is developed. Moreover, the G-STBC codeword is designed and a G-STBC codeword selection criterion that minimizes the BER performance under the constraints of a fixed spectral efficiency and total transmit power is then proposed. The selection index of the G-STBC codeword and the associated modulation type are determined at the receiver and conveyed to the transmitter with a limited feedback overhead to choose an appropriate mode for transmission. Finally, Numerical examples are used for illustrating the performance of the proposed G-STBCs, OSIC based detection and G-STBC codeword selection criterion.