Gaussian Mixture Models are among the most statistically mature methods which are used to make statistical inferences as well as performing unsupervised clustering. Formally, a gaussian mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the data set. In this paper, a probabilistic clustering based on the finite mixture models of the data distribution is suggested. An important issue in the finite mixture model-based clustering approach is to select the number of mixture components of clusters. In this sense, we focus on statistical inference for finite mixture models and illustrate how the variational Bayesian approach can be used to determine a suitable number of components in the case of a mixture of Gaussian distributions.