Sound source localization is one of the basic and essential techniques for intelligent robots in terms of human-robot interaction and has been utilized in various engineering fields. This paper suggests a new localization method using an inter-channel time difference trajectory, which is a new localization cue for efficient 3-D localization. As one of the ways to realize the proposed cue, a two-channel rotating array is employed. Two microphones are attached on the left and right sides of the spherical head. One microphone is in a circular motion on the right side, while the other is fixed on the left side. According to the rotating motion of the array, the (source) direction-dependent characteristics of the trajectories are analysed using the Ray-Tracing formula extended for 3-D models. In simulation, the synthesized signals generated by the fixed and rotating microphone signal models were used as the output signals of the two microphones. The simulation showed that the localization performance is strongly dependent on the azimuthal position of a source, which is caused by the asymmetry of the trajectory amplitude. Additionally, the experimental results of the two experiments carried out in the room environment demonstrated that the proposed system can localize a Gaussian noise source and a voice source in 3-D space.