The paper presents a novel algorithm for restoration of the missing samples in additive Gaussian noise based on the forward–backward autoregressive (AR) parameter estimation approach and the extrapolation technique. The proposed algorithm is implemented in two consecutive steps. In the first step, the forward–backward approach is used to estimate the parameters of the given neighbouring segments, while in the second step the extrapolation technique for the segments is applied to restore the samples of the missing segment. The experimental results demonstrate that the restoration error of the samples of the missing segment using the proposed algorithm is reduced as compared with the Burg algorithm.