Nowadays, Multicarrier Direct sequence code division multiple access (MC DS-CDMA) systems are used in mobile communication. Performance of these systems are limited by multiple access interference (MAI) created by spread-spectrum users in the channel as well as background channel noise. This paper proposes an incremental gradient descent (IGD) multi-user detection (MUD) for MC DS-CDMA system that can achieve near-optimum performance while the number of users is linear in its implementation complexity. The IGD algorithm make an effort to perform optimum MUD by updating one user's bit decision each iteration in the best way. This algorithm accelerates the gradient algorithm convergence by averaging. When a minimum mean square error (MMSE) MUD is employed to initialize the proposed algorithm, in all cases tested the gradient search converges to a solution with optimum performance. Further, the iterative tests denote that the proposed IGD algorithm provides significant performance for cases where other suboptimum algorithms perform poorly. Simulation compares the proposed IGD algorithm with the conventional detectors.