Recently, a block spreading code division multiple access (BS-CDMA) technique was presented, whereby user-specific precoding along with orthogonal spreading codes is used to achieve multiuser interference- (MUI-) free reception when all users arrive at the base station simultaneously. In practice, however, imperfect synchronization destroys the orthogonality among users, and MUI occurs. To mitigate the MUI in BS-CDMA due to quasisynchronous reception, this paper proposes an iterative successive interference cancellation (SIC) receiver, where cancellation of interfering signals is ordered according to the times of arrival (TOA) of the signals from different users. The ordering criterion is justified through analysis and simulation on the average signal-to-interference-plus-noise ratio (SINR) of different users, where it is shown that in a quasisynchronous BS-CDMA system, ordering with regard to increasing TOA is equivalent to ordering with respect to decreasing average SINR, when practical channels such as the exponentially decaying channel is considered. The proposed SIC receiver is shown to achieve a performance close to a system with synchronous reception for only two iterations. In addition, an algorithm to determine the detection order of different blocks is proposed such that parallel detection of the signals from different users with reduced latency can be achieved.