Lensless digital holography (LDH) is gaining considerable attention lately due to a simple experimental setup, wide field-of-view, and three-dimensional (3D) imaging capability. Since the resolution of LDH is limited by the Nyquist frequency of a detector array, the major drawback of LDH is resolution, and a lot of efforts were made to enhance the resolution of LDH. Here we propose and demonstrate a fast noniterative sub-pixel shifting super-resolution technique that can effectively enhance the resolution of LDH by a factor of two. We provide detailed frequency-domain formulae for our noniterative frequency-domain super-resolution method. The validity of our proposed method is experimentally demonstrated both for scattering and phase objects.