This paper describes a Bayesian network approach for modeling discrete travel choice problems. Bayesian networks are a marriage between probabilistic theory and graph theory. In a Bayesian network, the graphical network topology specifies the model structure while conditional probability distributions provide a mechanism to represent the probabilistic causal relationships between variables. Though this modeling tool is extensively used in many scientific areas for data causality or correlation analyses, no formal statement has been made on how to specify and estimate a Bayesian network for generic discrete choice modeling problems. In this paper, our particular interest is on the structure estimation of a discrete Bayesian network model in the context of travel choice prediction. The feature of a Bayesian network model, which allows its network structure to be estimated by combining both cause-effect hypotheses and observational information, enhances its capability in modeling complex travel choice patterns that existing models with a linear structure may not capture. Through a mode choice example for work trips, we demonstrate the model's advantages and disadvantages in this kind of applications.