Abstract: To overcome the problem that the performance of the traditional linear prediction (LP) analysis of speech deteriorates significantly in the presence of background noise, a novel algorithm for robust LP analysis of speech based on super-Gaussian excitation was proposed. The excitation noise of LP was modeled as a Student-t distribution, which was shown to be super-Gaussian. Then a novel probabilistic graphical model for robust LP analysis of speech was built by incorporating the effect of additive noise explicitly. Furthermore, variational Bayesian inference was adopted to approximate the intractable posterior distributions of the model parameters, based on which the LP coefficients of the noisy speech were estimated iteratively. The experimental results show that the developed algorithm performs well in terms of LP coefficients estimation of speech and is much more robust to ambient noise than several other algorithms.