Due to developments in video technology, the study of three-dimensional sound-field reproduction has recently gained attention. A virtual-sound-source (VSS) construction method using multiple parametric-array loudspeakers (PALs), which have sharper directivity, was previously proposed. With this method, multiple PAL units (called PAL array) are used and a VSS is presented with a fixed radiation direction at any point in the air. However, this method requires rearrangement of the PAL array to change the position of the VSS. Thus, in this paper, a VSS-construction method based on radiation direction control using the PAL array is proposed. The proposed method can reconstruct positions and radiation directions of VSSs without rearranging the PAL array. Specifically, the proposed method involves mounting pan and tilt units onto PAL units and electrically controlling their placement angles to focus the acoustic beams from them to the VSS positions. The proposed method also involves controlling the radiation direction of a VSS by weighting the output signal of each PAL unit to simulate the radiation direction of the real sound source. The effectiveness of the proposed method is confirmed through objective and subjective experiments.