The goal of this study is to equip a mobile service robot with an ability to navigate to the human who commands the robot by speech. This paper proposes a Bayesian approach to sound source localization for speaker tracking module. Based on time delay of arrival (TDOA) features, sound source direction is classified using a naïve Bayesian network. The method requires low computational complexity and is feasible for real-time robot navigation. Based on an experiment with various parameter settings in an indoor environment, different factors that affect the classification accuracy have been analyzed. Further validation on a human speaker with random sound volumes and positions illustrates that the proposed method can work efficiently in real-world environments.