We present a new space-time successive interference cancellation (ST-SIC) scheme with multiple transceiver antennas for direct-sequence code division multiple access (DS-CDMA) systems. The proposed scheme is computationally very efficient, while maintains the performance close to the previous space-time multiuser detection (ST-MUD) scheme. The bit error rate (BER) performance of the ST-SIC scheme for coherent phase shift keying (PSK) modulation is analytically examined in Rayleigh fading channels, and its validity and usefulness are demonstrated by computer simulations.