This paper proposes fuzzy gain scheduling of proportional differential control (FGS-PD) system for tracking mobile robot to moving sound sources. Given that the target positions of the real-time moving sound sources are dynamic, the mobile robots should be able to estimate the target points continuously. In such a case, the robots tend to slip owing to abnormal velocities and abrupt changes in the tracking path. The selection of an appropriate curvature along which the robot follows a sound source makes it possible to ensure that the robot reaches the target sound source precisely. For enabling the robot to recognize the sound sources in real time, three microphones are arranged in a straight formation. In addition, by applying the cross correlation algorithm to the time delay of arrival base, the received signals can be analyzed for estimating the relative positions and velocities of the mobile robot and the sound source. Even if the mobile robot is navigating along a curved path for tracking the sound source, there could be errors due to the inertial and centrifugal forces resulting from the motion of the mobile robot. Velocities of both robot wheels are controlled using FGS-PD control to compensate for slippage and to minimize tracking errors. For experimentally verifying the efficacy of the proposed the control system with sound source estimation, two mobile robots were fabricated. It was demonstrated that the proposed control method effectively reduces the tracking error of a mobile robot following a sound source.