One important class of state emission densities of the hidden Markov model (HMM) is the Gaussian mixture densities. The classical Baum-Welch algorithm often fails to reliably learn the Gaussian mixture densities when there is insufficient training data, due to the large number of free parameters present in the model. In this paper, we propose a novel strategy for robustly and accurately learning the Gaussian mixture state emission densities of the HMM. The strategy is based on an ensemble framework for probability density estimation in which the learning of the Gaussian mixture densities is formulated as a gradient descent search in a function space. The resulting learning algorithm is called "the boosting Baum-Welch algorithm." Our preliminary experiment results on emotion recognition from speech show that the proposed algorithm outperforms the original Baum-Welch algorithm on this task.