By adopting in-line lensless Fourier setup and phase-shifting technique, we recorded the phase-shifting digital hologram at short distance. As the Fresnel diffraction condition is no longer valid, the convolution approach is chosen for the reconstruction. However, the simulated reference wave for the reconstruction would suffer from severe under-sampling due to the comparatively large pixel size. To solve this problem, sine-interpolation is introduced to get the pixel-size of the hologram reduced prior to the reconstruction. The experimental results show that an object image of high fidelity is obtained with this method.