In this paper, performance of a novel interference cancellation technique for the single user detection in a direct-sequence code-division multiple access (DS-CDMA) system has been investigated. This new algorithm is based on the Cycle-and-Add property of PN (Pseudorandom Noise) sequences and can be applied for both synchronous and asynchronous systems. The proposed strategy provides a simple method that can delete interference signals one by one in spite of the power levels of interferences. Therefore, it is possible to overcome the near-far problem (NFP) in a successive manner without using transmit power control (TPC) techniques. The validity of the proposed procedure is corroborated by computer simulations in additive white Gaussian noise (AWGN) and frequency-nonselective fading channels. Performance results indicate that the proposed receiver outperforms the conventional receiver and, in many cases, it does so with a considerable gain.