In a compact digital lensless inline holographic microscope (LIHM), where the sample-to-sensor distance is short, the imaging resolution is often limited by sensor pixel size instead of the system numerical aperture. We propose to solve this problem by applying data interpolation with an iterative holographic reconstruction method while using grating illumination in the LIHM system. In the system setup, the Talbot self-image of a Ronchi grating was used to illuminate the sample, and the inline hologram was recorded by a CMOS imaging sensor located behind the sample. The hologram was then upsampled by data interpolation before the reconstruction process. In the iterative holographic reconstruction, the sample support was defined by the bright areas of the grating illumination pattern and was used as constraint. A wide-field image can also be obtained by shifting the grating illumination pattern. Furthermore, we assumed that the sample was amplitude object, i.e., no obvious phase change was caused by the sample, which provided additional constraint to refine the interpolated data values. Besides improved resolution, the iterative holographic reconstruction also helped to reduce the twin-image background. We demonstrated the effectiveness of our method with simulation and imaging experiment by using the USAF target and polystyrene microspheres with 1 μm diameter as the sample.