Past research has demonstrated that if the intensity image of an object is uniformly down-sampled and converted into a Fresnel hologram, the phase component alone will be sufficient to reconstruct the source image. However, due to down-sampling, the edge and line patterns are degraded heavily. In this Letter, we propose an enhancement on the parent method by incorporating an adaptive down-sampling lattice. A hologram generated with our proposed method, which is referred to as the edge-enhanced sampled phase-only hologram, preserves favorable visual quality on both the shaded regions as well as the edge patterns of the object image.