The multiple access causes an interference problem in the direct-sequence code-division multiple access systems. An efficient adaptive algorithm should be used to suppress this interference for the improvement of system performance. In this paper, the new blind adaptive method is suggested using the constant modulus algorithm for the purpose of interference suppression. Simulation results show that the converged value of signal to interference ratio for the proposed method is approximately 6 [dB] larger than that of a conventional Blind-MOE receiver in the additive white Gaussian noise channel and channel with inter-symbol interference while the signal to interference ratio improvement is almost 4 [dB] better in the Rayleigh fading channel. The suggested method is also robust to the new user interference resulting the nearly 3 [dB] improvement of the SIR value comparing with the conventional receiver. Based on these results, it is shown that the BER of the proposed receiver is lower than that of any other conventional receiver. Therefore, using the newly suggested method, the considerable performance improvement can be obtained for the DS-CDMA systems.