This paper presents a novel interference cancellation (IC) scheme for both synchronous and asynchronous direct-sequence code-division multiple-access (DS-CDMA) wireless channels. In the DS-CDMA system, the multiple access interference (MAI) and the near-far problem (NFP) are the two factors which reduce the capacity of the system. In this paper, we propose a new algorithm that is able to detect all interference signals as an individual MAI signal by maximum correlation detection. It is based on the discovery of all the unknowing spreading codes of the interference signals. Then, all possible MAI patterns so called replicas are generated as a summation of interference signals. And the true MAI pattern is found by taking correlation between the received signal and the replicas. Moreover, the receiver executes MAI cancellation in a successive manner, removing all interference signals by single-stage. Numerical results will show that the proposed IC strategy, which alleviates the detrimental effect of the MAI and the near-far problem, can significantly improve the system performance. Especially, we can obtain almost the same receiving characteristics as in the absense of interference for asynchrnous system when received powers are equal. Also, the same performances can be seen under any received power state for synchronous system.