As a data transmission rate must be increased as required to support the future high-speed wireless communication systems under multipath fading, the conventional DS-CDMA scheme suffers considerably from an intensive processing requirement for the increased spreading rate to combat the inter-chip interference (ICI) and furthermore, from the intersymbol interference (ISI) as the symbol duration becomes less than the channel delay spread. In this paper, a multi-carrier parallel combinatory DS-CDMA (MC-PC-CDMA) scheme is considered as one possible variant access scheme to realize a bandwidth efficient transmission for high transmission rate while maintaining the beneficial features of the DS-CDMA scheme. This scheme combines the parallel combinatory signaling feature of the existing parallel combinatory CDMA (PC-CDMA) scheme with the orthogonal carrier multiplexing feature of multi-carrier modulation so as to improve the bandwidth efficiency and to reduce the self-interference among the parallel spreading sequences of each user, respectively. This particular system configuration also treats the previously proposed multi-carrier DS-CDMA systems as a special case. Our analysis of the bit error rate for the asynchronous CDMA system investigates the performance characteristics of the proposed system on varying design parameters, and shows the performance comparison with other types of multi-carrier DS-CDMA systems.