Recent space plasma observations have provided us with three-dimensional velocity distributions having multiple peaks. We propose a method for analyzing such velocity distributions via a multivariate Maxwellian mixture model where each component of the model represents each of the multiple peaks. The parameters of the model are determined through the Expectation-Maximization (EM) algorithm. For the automatic judgment of the preferable number of components in the mixture model, we introduce a method of examining the number of extrema of a resulting mixture model. We show applications of our method to velocity distributions observed in the Earth's magnetotail.