In 1990 Vijayan and Poor proposed nonlinear predictive methods for suppressing narrowband interference in spread spectrum (SS) systems with a significant increase in signal-to-noise ratio (SNR) improvement The main drawback of their adaptive nonlinear filter is its slow convergence rate. A new adaptive least mean squares (LMS) algorithm to increase the slow convergence rate of their nonlinear adaptive filter is described. Computer simulation results are presented to support the advantages of the new filter. © 1995, IEEE. All rights reserved.