The performance of linear prediction analysis of speech deteriorates rapidly under noisy environments.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 additive noise is incorporated explicitly to increase the robustness,thus a probabilistic model for sparse linear prediction of speech is built.Furthermore,variational Bayesian inference is utilized to approximate the intractable posterior distributions of the model parameters,and then 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 the traditional algorithm and the l_1 norm minimization based sparse linear prediction algorithm proposed in recent years.Finally it draws to a conclusion that the proposed algorithm is more robust to noise and is able to increase the speech quality in applications. The performance of linear prediction analysis of speech deteriorates rapidly under noisy environments. 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 additive noise is incorporated explicitly to increase the robustness, thus a probabilistic model for sparse linear prediction of speech is built. F urthermore, variational Bayesian inference is utilized to approximate the intractable posterior distributions of the model parameters, and the 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 the traditional algorithm and the l_1 norm minimization based sparse linear prediction algorithm proposed in recent years. Finally it draws to a conclusion that the proposed algorithm is more robust to noise and is able to increase t he speech quality in applications.