This paper addresses the problem of accurately realizing the interpolation of spatially discrete head-related transfer function (HRTF) for synthesis of virtual auditory space. By analyzing the advantages and disadvantages of general bilinear interpolation method in 3D-sound, associating with human auditory system's mechanism of band-pass filtering and consulting critical bands of psychoacoustics, the paper presents a piecewise interpolation method based on log-least square error criterion for HRTF's magnitude to compensate the deficiency of bilinear method in intermediate frequency. As seen from the following simulations, this new method accomplishes preferable results.