In this paper, a novel low-complexity sphere decoding (SD) algorithm (QSM-Tx) designed for quadrature spatial modulation (QSM) is proposed. The reduction of the computational complexity for QSM-Tx is achieved by only searching the specific points lying inside the given sphere rather than all possible points for maximum likelihood (ML) detection. And the bit-error-rate (BER) performance for the proposed QSM-Tx remains close to the ML algorithm. Furthermore, a modified sphere decoding for QSM, called QSM-Rx, with low complexity and the optimum BER performance is presented as well. Finally, the validity of the proposed QSM-Tx scheme is verified by simulation results.