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In this paper a new robust recursive method of estimating the linear prediction parameters of an auto-regressive speech signal model using weighted least squares with variable forgetting factors (VVFs) is described. The proposed robust recursive least-squares (RRLS) method differs from the conventional recursive least-squares (RLS) method by the insertion of a suitably chosen nonlinear transformation of the prediction residuals. The RRLS algorithm takes into account the contaminated Gaussian nature of the excitation for voiced speech, and the effect of nonlinearity is to assign less weight to the small portions of large residuals so that the spiky excitation will not greatly influence the final AR parameter estimates, while giving unity weight to the bulk of small to moderate residuals generated by the nominal Gaussian distribution. In addition, the VFF is adapted to a nonstationary speech signal by a generalized likelihood ratio algorithm, which accounts for the nonstationarity of a speech signal. The proposed method has a good adaptability to the nonstationary parts of a speech signal, and gives low bias and low variance at the stationary signal segments. The feasibility of the robust approach is demonstrated with both synthesized and natural speech. © 1995.