As a basic study into 3-D audio display systems, this paper reports the conditions of moving sound image velocity and time-step where a discrete moving sound image is perceived as continuous motion. In this study, the discrete moving sound image was presented through headphones and ran along the ear-axis. The experiments tested the continuity of a discrete moving sound image using various conditions of velocity (0.25, 0.5, 0.75, 1, 2, 3, and 4 m/s) and time-step (0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, and 0.14 s). As a result, the following were required in order to present the discrete moving sound image as continuous movement. (1) The 3-D audio display system was required to complete the sound image presentation process, including head tracking and HRTF simulation, in a time shorter than 0.02 s, in order to present sound image movement at all velocities. (2) A processing time longer than 0.1 s was not acceptable. (3) If the 3-D audio display system only presented very slow movement (less than about 0.5 m/s), processing times ranging from 0.04 s to 0.06 s were still acceptable.