The transmission structure of quadrature spatial modulation (QSM) restricts the signal constellation to be lattice style. Meanwhile, both the minimum amplitude and minimum Euclidean distance (MED) in quadrature and in-phase domain should be taken into account for the constellation design of QSM. In this paper, a non-uniform lattice constellation is designed for quadrature spatial modulation (QSM), which provides noticeable performance gains compared to the uniform quadrature amplitude modulation (QAM) that is designed only based on the MED of constellation. The analysis and simulation results show that the gains over uniform QAM become more notable as the number of transmit antennas increases.