In this paper we propose a new algorithm based on third order cumulants, for MultiCarrier Code Division Multiple Access (MC-CDMA) system equalization. In order to test its efficiency, we have compared with the (CUM-AZ) algorithm proposed in the literature, for that we considered five practical frequency-selective fading channels, called Broadband Radio Access Network (BRAN A, BRAN B, BRAN C, BRAN D, and BRAN E), normalized for (MC-CDMA) system, excited by non-Gaussian sequences. In the part of (MC-CDMA), we use the zero forcing (ZF) and the minimum mean square error (MMSE) equalizers techniques after the channel identification to correct the channel's distortion. The simulation results, in noisy environment and for different signal to noise ratio (SNR), are presented to illustrate the performance of the proposed algorithm.