Abstract: The performance of linear prediction analysis of speech deteriorates rapidly under noisy environment. To tackle this issue, an improved noise-robust sparse linear prediction algorithm is proposed. First, the linear prediction residual of speech is modeled as Student-t distribution, and the influence of additive noise is incorporated explicitly so as to increase the robustness, thus a complete probabilistic model of the proposed algorithm is built. Furthermore, variational Bayesian inference is utilized to approximate the intractable posterior distributions of the model parameters, based on which the optimal linear prediction parameters are estimated robustly. The experimental results demonstrate the advantage of the developed algorithm in terms of several different metrics compared with traditional algorithm and the l₁ norm minimization based sparse linear prediction algorithm proposed in recent years. It is shown that the proposed algorithm is more robust to noise and with less distortion, and thus increases the speech quality in applications with ambient noise.