Heavy computational complexity and imprecise reconstruction of objects are crucial problems in computer-generated holograms. In this paper, we propose a non-uniform sampling based on novel compressed look up table method to generate holograms. The method consists of two steps: in the first step, the non-uniform basic modulation factors are precalculated and stored in look-up-table. Secondly, fringe patterns for other points are obtained by simply shifting and multiplying the pre-calculated non-uniform basic modulation factors, and the final computer-generated hologram is obtained by adding them all together. The proposed method eliminates the redundant information properly and modulates the reconstructed images precisely. Numerical simulation results show proposed method reduces the memory usage, speeds up computation time and the quality of reconstructed images do not degrade evidently compared with uniform sampling method. Optical experiments results are in good agreement with numerical simulation results. The proposed method is simple, effective and could be applied in the holographic field in the future.