It is suggested that the curvature trajectory be used to estimate the real-time moving sound sources and efficiently the robot estimating the sound sources. Since the target points of the real-time moving sound sources change, the mobile robot continuously estimates the changed target points. In such a case, the robot experiences a slip phenomenon due to the abnormal velocity and the changes of the navigating state. By selecting an appropriate curvature and navigating the robot gradually by using it, it is possible to enable the robot to reach the target points without having much trouble. In order to recognize the sound sources in real time, three microphones need to be organized in a straight form. Also, by applying the cross-correlation algorithm to the TDOA base, the signals can be analyzed. By using the analyzed data, the locations of the sound sources can be recognized. Based on such findings, the sound sources can be estimated. Even if the mobile robot is navigated by selecting the gradual curvature based on the changed target points, there could be errors caused by the inertia and the centrifugal force related to the velocity. As a result, it is possible to control the velocity of both wheels of the robot through the velocity PID controller in order to compensate for the slip phenomenon and minimize the estimated errors. In order to examine whether the suggested curvature trajectory is appropriate for estimating the sound sources, two mobile robots are arranged to carry out an actual experiment. The first robot is moved by discharging the sound sources, while the second robot recognizes and estimates the locations of the discharged sound sources in real time.