Latent class models have recently drawn considerable attention among many researchers and practitioners as a class of useful tools for capturing heterogeneity across different segments in a target market or population. In this paper, we consider a latent class logit model with parameter constraints and deal with two important issues in the latent class models - parameter estimation and selection of an appropriate number of classes - within a Bayesian framework. A simple Gibbs sampling algorithm is proposed for sample generation from the posterior distribution of unknown parameters. Using the Gibbs output, we propose a method for determining an appropriate number of the latent classes. A real-world marketing example as an application for market segmentation is provided to illustrate the proposed method.