High efficiency phase holograms are designed and implemented using aperiodic two-dimensional (2D) high-contrast gratings (HCGs). With our design algorithm and an in-house developed rigorous coupled-wave analysis (RCWA) package for periodic 2D HCGs, the structural parameters are obtained to achieve a full 360-degree phase-tuning range of the reflected or transmitted wave, while maintaining the power efficiency above 90%. For given far-field patterns or 3D objects to reconstruct, we can generate the near-field phase distribution through an iterative process. The aperiodic HCG phase plates we design for holograms are pixelated, and the local geometric parameters for each pixel to achieve desired phase alternation are extracted from our periodic HCG designs. Our aperiodic HCG holograms are simulated using the 3D finite-difference time-domain method. The simulation results confirm that the desired far-field patterns are successfully produced under illumination at the designed wavelength. The HCG holograms are implemented on the quartz wafers, using amorphous silicon as the high-index material. We propose HCG designs at both visible and infrared wavelengths, and our simulation confirms the reconstruction of 3D objects. The high-contrast gratings allow us to realize low-cost, compact, flat, and integrable holograms with sub-micrometer thicknesses.