To follow a sound source by a mobile robot, the relative position and orientation of the sound source from the mobile robot have been estimated using a microphone array. In this research, the difference among the traveling times of the sound source to each of three microphones has been used to calculate the distance and orientation of the sound source from the mobile robot which carries the microphone array. The cross-correlation between two signals has been applied for detecting the time difference between two signals, which provides reliable and precise value of the time difference comparing to the conventional methods. To generate the tracking direction to the sound source, fuzzy rules are applied and the results are used to control the mobile robot in a real-time. The efficiency of the proposed algorithm has been demonstrated through the real experiments comparing to the conventional approaches.