For three-dimensional (3D) ultrasound imaging, to obtain a 3D image with sufficient resolution, the inter-channel spacing (i.e., pitch) should be sufficiently small to avoid grating lobes and the aperture size needs to be large enough to ensure that the beam width is sufficiently small. Therefore, a matrix probe often consists of several thousands of channels resulting in requiring high system complexity. The sparse array (SA) method has been proposed to reduce the system complexity by selecting a set of active channels instead of fully-sampled channels; however, SA approach encounters focusing errors during beamforming which results in broadening the main lobe, as well as increasing the side-lobe and grating-lobe levels, which together degrade the image quality. In this study, a deep variational network has been presented to reconstruct the inactive channels for the sparse array system. The main advantage of the deep variational network is that this method can be trained with a comparably low number of training cases. This can be beneficial for medical 3-D/4-D ultrasound imaging reconstruction because large amount of raw 3D ultrasound RF channel data are not easy to acquire. In this study, 512 under-sampled channels were set as active by sampling 1024 channels uniformly. The fully sampled channel data (output) were captured as the ground truth using a 2-D matrix array. With the proposed method, the output image can improve the grating-lobe levels by 12.27 dB and 4.76 dB, respectively, for both the elevation and lateral projections.